Complement Rebuttal
*Sorry for the split of our rebuttal due to the character limit.*
# Why "alignment" is related to fast-adaptation? Isn't fast adaptation related to the number of steps to converge, not the number of shots?
**Reply.**
From the perspective of gradient-based meta-learning methods, "fast" can be interpreted as "few steps" to converge. From a more general perspective of meta-learning, "fast" could be interpreted as "few-shot", for the following reasons: In real world application of machine learning, the accumulation of labeled data takes time; Apart from gradient-based methods, other meta-learning methods do not have the concept of "steps" for adaptation; Early meta-learning works take shots as sequential input (e.g., with RNN, memorization), thus temporal fast means short sequence, corresponding to few-shot.
"Alignment" is mapping the representations of a positive pair together in contrastive learning [paper-ref 48], thus be (mostly) invariant to unneeded noise factors. In ConML, this means aligning model generated by the meta-leaner with different subsets of the same task (line 140~143), by minimizing $D^{in}$ (eqn.(2)). This encourage the model generated with few-shot to be similar with fully-supervised ones. The meta-learner thus can learn noise- and bias-invariant task knowledge from few-shot.
Experiment results in Fig.2(c) verifies "alignment" is related to fast-adaptation.
# Why "discrimination" is related to the generalization?
**Reply.**
"Discrimination" is maximizing intra-task distance, i.e., distance between negative pairs in contrastive learning (line).
Meta-learning aims at improving the performance on unseen tasks. With a natural supposition that different tasks enjoy different task-specific models, discrimination, i.e., meta-learner can learn different
models from different tasks, is important for task-level generalizability.
Experiment results in Fig.2(f) verifies "discrimination" is related to task-level generalization.
This objective also plays the role as an offset of the inner-task distance. In fact, this objective can be not optimized explicitly but through serving as negative pairs to optimize the softmax value in InfoNCE in *Common Reply 2* and obtain better performance.
# Illustration about experiment results and details.
**Reply.**
Due to the page limit, details about experiment settings have been presented as short as possible (e.g., "following the same settings in [17]", "Following [18]"). We apologize for the difficulty in reading. However, we hope the omission of unmentioned details would not trouble the understanding of the experiment results, and code for all experiments is provided in appendix. We would like to provide full details in appendix later.
As for section 5.1, we provide analysis about statistical results comparing meta-training MAML with different meta-objectives (MAML, in-MAML, out-MAML, ConML-MAML).
Result 1: Comparing Fig.2(a) and (d), which are t-sne visualization of model representations, along with the clustering performance in Table 2, ConML do align and discriminate the model representation as expected.
Result 2: Fig.2(b) and (e) (x-axis: cosine distance value, y-axis: count) show the distribution of inner-task and inter-task distance respectively, meta-trained by the four variants. We can find that: the alignment and discrimination ability corresponds to optimizing inner- and inter-task distance respectively; the alignment and discrimination capabilities are generalizable; ConML shows the couple of both capabilities.
Result 3: Fig.2(c) shows the testing performance varying shots number (x-axis: shot, y-axis: Relative Error (/MAML)). We find alignment is closely related to the fast-adaptation ability of the meta-learner.
Result 4: Fig.2(f) shows the testing performance varying the distribution of sine parameter (x-axis: Distribution Shift, y-axis: Relative Error (/MAML)). We find discrimination is closely related to the task-level generalizability.
# Ablation studies.
**Reply.**
Please refer to *Common Reply 2*.