MT-CC: Multi-Group Temperature Scaling for Asymmetric Calibration Behavior in Class-Incremental Learning
Organizations: Yonsei University
Abstract
As deep neural networks are required to continuously adapt to evolving data, class-incremental learning (CIL) has become an active research area. However, most existing works primarily focus on improving accuracy while overlooking confidence calibration, which measures the trustworthiness of the model's predictions. Although temperature scaling (TS) is effective for static calibration, it has rarely been explored in continual settings where data distributions evolve over time. In this paper, we introduce Multi-Group Temperature Scaling for Continual Calibration (MT-CC), a novel post-hoc calibration framework that addresses the asymmetric calibration behavior in CIL, where the rate of confidence changes does not align with the rate of accuracy degradation across tasks, leading to different levels of miscalibration. Our key contribution is to design multiple temperature parameters through a lightweight grouping network that separates samples by confidence statistics and task-aware signals in CIL. Furthermore, a Groupwise Difference-between-Confidence-and-Accuracy (GDCA) regularization is incorporated to promote intra-group consistency. Experiments demonstrate that MT-CC significantly improves calibration performance while maintaining accuracy, offering a principled framework for reliable continual learning.
Figures & tables
| Replay buffer | 5K | 10K | 20K | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| CL | CA | ECE( ) | AECE( ) | SCE( ) | ECE( ) | AECE( ) | SCE( ) | ECE( ) | AECE( ) | SCE( ) |
| ER | Vanilla | 29.95\raisebox{0.0pt}{\scriptsize\pm 0.30} | 29.95\raisebox{0.0pt}{\scriptsize\pm 0.30} | 2.18\raisebox{0.0pt}{\scriptsize\pm 0.02} | 22.46\raisebox{0.0pt}{\scriptsize\pm 0.19} | 22.46\raisebox{0.0pt}{\scriptsize\pm 0.19} | 1.80\raisebox{0.0pt}{\scriptsize\pm 0.02} | 16.39\raisebox{0.0pt}{\scriptsize\pm 0.23} | 16.38\raisebox{0.0pt}{\scriptsize\pm 0.23} | 1.45\raisebox{0.0pt}{\scriptsize\pm 0.02} |
| TS [ 12 ] | 29.66\raisebox{0.0pt}{\scriptsize\pm 0.33} | 29.63\raisebox{0.0pt}{\scriptsize\pm 0.33} | 2.16\raisebox{0.0pt}{\scriptsize\pm 0.02} | 22.67\raisebox{0.0pt}{\scriptsize\pm 0.17} | 22.65\raisebox{0.0pt}{\scriptsize\pm 0.18} | 1.79\raisebox{0.0pt}{\scriptsize\pm 0.02} | 16.83\raisebox{0.0pt}{\scriptsize\pm 0.18} | 16.80\raisebox{0.0pt}{\scriptsize\pm 0.20} | 1.44\raisebox{0.0pt}{\scriptsize\pm 0.01} | |
| ETS [ 50 ] | 30.68\raisebox{0.0pt}{\scriptsize\pm 0.25} | 30.65\raisebox{0.0pt}{\scriptsize\pm 0.26} | 1.09\raisebox{0.0pt}{\scriptsize\pm 0.01} | 23.53\raisebox{0.0pt}{\scriptsize\pm 0.16} | 23.53\raisebox{0.0pt}{\scriptsize\pm 0.16} | 1.09\raisebox{0.0pt}{\scriptsize\pm 0.01} | 17.62\raisebox{0.0pt}{\scriptsize\pm 0.22} | 17.58\raisebox{0.0pt}{\scriptsize\pm 0.23} | 0.91\raisebox{0.0pt}{\scriptsize\pm 0.00} | |
| PTS [ 42 ] | 30.32\raisebox{0.0pt}{\scriptsize\pm 0.44} | 30.32\raisebox{0.0pt}{\scriptsize\pm 0.44} | 1.09\raisebox{0.0pt}{\scriptsize\pm 0.01} | 22.79\raisebox{0.0pt}{\scriptsize\pm 0.36} | 22.80\raisebox{0.0pt}{\scriptsize\pm 0.36} | 1.89\raisebox{0.0pt}{\scriptsize\pm 0.01} | 16.52\raisebox{0.0pt}{\scriptsize\pm 0.27} | 16.51\raisebox{0.0pt}{\scriptsize\pm 0.28} | 0.91\raisebox{0.0pt}{\scriptsize\pm 0.01} | |
| T-CIL [ 16 ] | 13.45\raisebox{0.0pt}{\scriptsize\pm 0.15} | 13.43\raisebox{0.0pt}{\scriptsize\pm 0.13} | 1.79\raisebox{0.0pt}{\scriptsize\pm 0.01} | 7.74\raisebox{0.0pt}{\scriptsize\pm 0.23} | 7.72\raisebox{0.0pt}{\scriptsize\pm 0.24} | 1.49\raisebox{0.0pt}{\scriptsize\pm 0.01} | 10.57\raisebox{0.0pt}{\scriptsize\pm 0.22} | 10.52\raisebox{0.0pt}{\scriptsize\pm 0.24} | 1.27\raisebox{0.0pt}{\scriptsize\pm 0.00} | |
Appendix figures & tables19 assets
Supplementary material from the paper’s appendix.
Appendix
| ECE | AECE | Brier | |
|---|---|---|---|
| 1 (T-CIL) | |||
| 2 | |||
| 3 | |||
| 4 | |||
| 5 |
| CIFAR-10 | CIFAR-100 | Tiny-ImageNet | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Method | ECE@15 | ECE@20 | Brier | ECE@15 | ECE@20 | Brier | ECE@15 | ECE@20 | Brier |
| T-CIL | 15.36\raisebox{0.0pt}{\scriptsize\pm 1.39} | 15.37\raisebox{0.0pt}{\scriptsize\pm 1.40} | 0.498\raisebox{0.0pt}{\scriptsize\pm 0.019} | 6.19\raisebox{0.0pt}{\scriptsize\pm 0.39} | 6.27\raisebox{0.0pt}{\scriptsize\pm 0.38} | 0.570\raisebox{0.0pt}{\scriptsize\pm 0.005} | 19.04\raisebox{0.0pt}{\scriptsize\pm 0.42} | 19.13\raisebox{0.0pt}{\scriptsize\pm 0.41} | 0.883\raisebox{0.0pt}{\scriptsize\pm 0.004} |
| T-CIL+ETS | 14.01\raisebox{0.0pt}{\scriptsize\pm 1.31} | 14.05\raisebox{0.0pt}{\scriptsize\pm 1.30} | 0.497\raisebox{0.0pt}{\scriptsize\pm 0.019} | 5.80\raisebox{0.0pt}{\scriptsize\pm 0.45} | 5.87\raisebox{0.0pt}{\scriptsize\pm 0.44} | 0.571\raisebox{0.0pt}{\scriptsize\pm 0.004} | 22.21\raisebox{0.0pt}{\scriptsize\pm 0.21} | 22.25\raisebox{0.0pt}{\scriptsize\pm 0.21} | 0.901\raisebox{0.0pt}{\scriptsize\pm 0.003} |
| T-CIL+IRM | 14.90\raisebox{0.0pt}{\scriptsize\pm 0.95} | 14.83\raisebox{0.0pt}{\scriptsize\pm 1.11} | 0.506\raisebox{0.0pt}{\scriptsize\pm 0.019} | 6.88\raisebox{0.0pt}{\scriptsize\pm 0.66} | 6.97\raisebox{0.0pt}{\scriptsize\pm 0.67} | 0.571\raisebox{0.0pt}{\scriptsize\pm 0.006} | 18.08\raisebox{0.0pt}{\scriptsize\pm 0.42} | 18.05\raisebox{0.0pt}{\scriptsize\pm 0.51} | 0.884\raisebox{0.0pt}{\scriptsize\pm 0.005} |
| T-CIL+AdaTS | 14.31\raisebox{0.0pt}{\scriptsize\pm 1.44} | 14.34\raisebox{0.0pt}{\scriptsize\pm 1.44} | 0.501\raisebox{0.0pt}{\scriptsize\pm 0.023} | 7.76\raisebox{0.0pt}{\scriptsize\pm 0.50} | 7.86\raisebox{0.0pt}{\scriptsize\pm 0.51} | 0.586\raisebox{0.0pt}{\scriptsize\pm 0.004} | 21.75\raisebox{0.0pt}{\scriptsize\pm 1.25} | 21.80\raisebox{0.0pt}{\scriptsize\pm 1.28} | 0.905\raisebox{0.0pt}{\scriptsize\pm 0.012} |
| MT-CC | 10.22\raisebox{0.0pt}{\scriptsize\pm 1.51} | 10.27\raisebox{0.0pt}{\scriptsize\pm 1.48} | 0.447\raisebox{0.0pt}{\scriptsize\pm 0.015} | 4.62\raisebox{0.0pt}{\scriptsize\pm 0.51} | 4.72\raisebox{0.0pt}{\scriptsize\pm 0.54} | 0.556\raisebox{0.0pt}{\scriptsize\pm 0.006} | 15.87\raisebox{0.0pt}{\scriptsize\pm 0.37} | 15.93\raisebox{0.0pt}{\scriptsize\pm 0.36} | 0.839\raisebox{0.0pt}{\scriptsize\pm 0.003} |
| Setting | Single-T ECE | MT-CC ECE |
|---|---|---|
| Static joint training | ||
| CIL (task average) |
| Method | Per-sample inference time ( s) | Relative |
|---|---|---|
| TS | 1250.41 | 1.0000 |
| PTS | 1250.65 | 1.0002 |
| AdaTS | 1252.63 | 1.0018 |
| MT-CC | 1250.80 | 1.0003 |
| Method | Calibration / Routing | Feature | ECE | AECE | Brier |
|---|---|---|---|---|---|
| PTS | Instance-wise TS | Top-10 logits | |||
| PTS | Instance-wise TS | CIL-aware features | |||
| AdaTS | Instance-wise TS | Penultimate feature | |||
| AdaTS | Instance-wise TS | CIL-aware features | |||
| GC+TS [ 45 ] | Semantic-aware learned grouping + group-wise TS | Penultimate feature | |||
| K-means Group-TS | K-means ( ) + group-wise TS | CIL-aware features |
| Setting | b0 | b1 | b2 | b3 | b4 | b5 | b6 | b7 | b8 | b9 |
|---|---|---|---|---|---|---|---|---|---|---|
| (low) | (high) | |||||||||
| Static | 1.98 | 1.99 | 2.00 | 1.95 | 2.00 | 1.94 | 1.96 | 1.92 | 2.04 | 2.10 |
| CIL | 1.58 | 1.68 | 1.77 | 1.84 | 2.00 | 2.13 | 2.36 | 2.59 | 2.99 | 3.82 |
| Setting | Margin region | Low-conf. | High-conf. | |
|---|---|---|---|---|
| Static | Low | 1.98 | 1.99 | 0.01 |
| High | 1.94 | 2.03 | 0.09 | |
| CIL | Low | 1.60 | 1.95 | 0.34 |
| High | 2.26 | 3.32 | 1.05 |
| ECE | Brier | ECE | Brier | ECE | Brier | ECE | Brier | |
|---|---|---|---|---|---|---|---|---|
| 50 | 4.77\raisebox{0.0pt}{\scriptsize\pm 0.43} | 0.565\raisebox{0.0pt}{\scriptsize\pm 0.009} | 4.92\raisebox{0.0pt}{\scriptsize\pm 0.50} | 0.573\raisebox{0.0pt}{\scriptsize\pm 0.006} | 5.00\raisebox{0.0pt}{\scriptsize\pm 0.43} | 0.573\raisebox{0.0pt}{\scriptsize\pm 0.006} | 5.98\raisebox{0.0pt}{\scriptsize\pm 0.48} | 0.572\raisebox{0.0pt}{\scriptsize\pm 0.004} |
| 100 | 4.36\raisebox{0.0pt}{\scriptsize\pm 0.46} | 0.560\raisebox{0.0pt}{\scriptsize\pm 0.007} | 4.69\raisebox{0.0pt}{\scriptsize\pm 0.40} | 0.571\raisebox{0.0pt}{\scriptsize\pm 0.005} | 4.81\raisebox{0.0pt}{\scriptsize\pm 0.45} | 0.571\raisebox{0.0pt}{\scriptsize\pm 0.006} | 5.78\raisebox{0.0pt}{\scriptsize\pm 0.30} | 0.571\raisebox{0.0pt}{\scriptsize\pm 0.005} |
| 250 | 4.49\raisebox{0.0pt}{\scriptsize\pm 0.45} | 0.558\raisebox{0.0pt}{\scriptsize\pm 0.006} | 4.70\raisebox{0.0pt}{\scriptsize\pm 0.27} | 0.572\raisebox{0.0pt}{\scriptsize\pm 0.005} | 4.73\raisebox{0.0pt}{\scriptsize\pm 0.34} | 0.572\raisebox{0.0pt}{\scriptsize\pm 0.006} | 5.74\raisebox{0.0pt}{\scriptsize\pm 0.33} | 0.570\raisebox{0.0pt}{\scriptsize\pm 0.005} |
| 500 | 4.54\raisebox{0.0pt}{\scriptsize\pm 0.56} | 0.557\raisebox{0.0pt}{\scriptsize\pm 0.006} | 4.72\raisebox{0.0pt}{\scriptsize\pm 0.41} | 0.571\raisebox{0.0pt}{\scriptsize\pm 0.006} | 4.71\raisebox{0.0pt}{\scriptsize\pm 0.37} | 0.571\raisebox{0.0pt}{\scriptsize\pm 0.006} | 5.83\raisebox{0.0pt}{\scriptsize\pm 0.30} | 0.571\raisebox{0.0pt}{\scriptsize\pm 0.005} |
| 1000 | 4.49\raisebox{0.0pt}{\scriptsize\pm 0.53} | 0.556\raisebox{0.0pt}{\scriptsize\pm 0.006} | 4.63\raisebox{0.0pt}{\scriptsize\pm 0.30} | 0.571\raisebox{0.0pt}{\scriptsize\pm 0.007} | 4.59\raisebox{0.0pt}{\scriptsize\pm 0.40} | 0.571\raisebox{0.0pt}{\scriptsize\pm 0.007} | 5.82\raisebox{0.0pt}{\scriptsize\pm 0.31} | 0.571\raisebox{0.0pt}{\scriptsize\pm 0.005} |
| Grouping-network strategy | ECE | AECE | SCE ( ) | Brier |
|---|---|---|---|---|
| MT-CC | ||||
| Lag-1 | ||||
| Fresh each task |
| Condition | G1 retention (%) | G2 retention (%) |
|---|---|---|
| Classifier and router change | ||
| Router change only |
| Routing behavior | w/o GDCA | with GDCA |
|---|---|---|
| Frequency of minority-group fraction below | ||
| Mean minority-group fraction |
| Dataset | After First Task | After Middle Task | After Final Task | |||
|---|---|---|---|---|---|---|
| Acc (%) | Conf (%) | Acc (%) | Conf (%) | Acc (%) | Conf (%) | |
| CIFAR-10 | ||||||
| CIFAR-100 | ||||||
| Tiny-ImageNet | ||||||
Model Calibration
Model calibration aligns predicted confidence or model outputs with observed outcomes and measurements to support more reliable decisions.
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