KC-EMA Mechanism: Theoretical Analysis and Derivation for IIL

Table of Links

Abstract and 1 Introduction

2. Related works

3. Problem setting

4. Methodology

   4.1. Decision boundary-aware distillation

   4.2. Knowledge consolidation

5. Experimental results and 5.1. Experiment Setup

   5.2. Comparison with SOTA methods

   5.3. Ablation study

6. Conclusion and future work and References

Supplementary Material

7. Details of the theoretical analysis on KCEMA mechanism in IIL
8. Algorithm overview
9. Dataset details
10. Implementation details
11. Visualization of dusted input images
12. More experimental results

7. Details of the theoretical analysis on KCEMA mechanism in IIL

In Sec. 4.3 of the manuscript, we theoretically analyze the feasibility of applying a model EMA-like mechanism in the IIL. Here, gives more derivation details of the Eq. 7.

The derivative of the old task(s) and the new task on the teacher model in current IIL phase is

Therefore, we get Eq. (7) and many conclusions can be drawn based on it as we present in the manuscript. Notably, as we assume the student is fully trained on new data, we set a freezing period during which we only train the student without implementing KC-EMA. In the manuscript, we empirically set the freezing period to 10 epochs.

Limitation. Our method may accumulate errors after a long consecutive IIL tasks. For example, in the ith IIL task, the old model should consider the base task and the previous i − 1 IIL task. The old task’s derivative on the parameters of teacher becomes