Further clarification on the problem setting
Dear Reviewer v3Yx,
Thank you for the comment. We agree with you on NPs for the meta-learning (ML) settings including few shot problems. To clarify the problem setting and your further questions, we have prepared the following three points whilst being more specific in terms of notations.
**A. ML vs CL (ours) setting:** In both ML and continual learning (CL) settings, we have multiple tasks and we would like to learn an NP to generate task-specific functions, which aligns with “NPs are trained as generative models of these functions in a way that enables flexible conditioning”. Specifically, for each task t, we have $Y = f_{Z_t}(X)$ and $Z_t$ is the latent variable conditioned on the task-specific contexts. As $Z_t$ is task-specific, this makes $f_{Z_t}$ also task-specific.
There are two major differences between standard NPs for ML and our proposed NP for CL:
1. In standard NPs, $Z_t$ is conditioned on $(X^c_t, Y^c_t)$, which are context samples of task $t$. While in our NP, $Z_t$ is conditioned on $(X^c_t, Y^c_t, Z_G)$. $Z_G$ is from $X^c_G, Y^c_G$ which are the data samples from all the tasks. To accommodate the properties of CL better, we introduce a hierarchical model that introduces more sharing in $f_{Z_t}$ across the tasks via $Z_G$.
2. The goals of ML and CL are quite different. ML aims to learn NPs that can generalize to new tasks. That is why NPs are tested in a new task $t*$ given its context samples $(X^c_t*, Y^c_t*)$. In CL, our goal is to have a good $f$ that can perform well on all the seen tasks. Therefore, there is no new task during inference. Similar to other works adapting NPs to learn such a good $f$ generalizing all the seen training tasks [1], our context samples during testing are a subset of the training data for the tasks seen so far.
To summarize, CL requires to learn a general function $f$ that is task-specific but also performs well on all the seen tasks given a limited rehearsal memory. To achieve this, we leverage NP ability of generating task-specific functions with flexible conditioning. But instead of using the standard model of NPs, we propose a hierarchical model to introduce more sharing, tailored for the CL problem.
**B. Task-to-function equivalence:** A CL task may or may not involve data points sampled from a single function $f_{Z_t}: x$->$y$. For a standard CL setup (like ours), the equivalence between a task and a function does hold since each data point $x$ in a task is mapped to a single label $y$. However, if we were to adapt NPs for a multi-label CL setting [3,4], then similar to [2], at each (incremental) training task, we would learn a function with a multi-dimensional output $y$.
You are thus correct that the tasks and functions are not equivalent in [2]. But for our CL setup, where each $x$ has a single label $y$, a task–to–function equivalence holds. In fact, we note the difference in the nature of prediction variables $y$ between ours and [2] in the related work **lines 84-85 (see point (b))** in the main paper. Based on this discussion, we will rephrase the line to make it more explicit regarding the equivalence.
**C. Limited context scenario:** Finally, just like the standard NPs, NPCL does not need a complete set of context points over all the learned functions to be able to infer these although a diverse set of context does certainly help. This is evident from our ablation on the varying context sizes during inference (lines 253-256 in main paper). Here, a context set size of as little as 5 still helps us maintain a competitive accuracy on S-CIFAR-10.
We hope the above points help clarify your doubts regarding the usage of NPs in our problem setting. Please let us know if you have any further questions or concerns.
We look forward to your feedback.
*References*:
[1] Wang, J., Lukasiewicz, T., Massiceti, D., Hu, X., Pavlovic, V., & Neophytou, A. (2022). NP-Match: When Neural Processes meet Semi-Supervised Learning. ICML.
[2] Kim, D., Cho, S., Lee, W., & Hong, S. (2022). Multi-Task Processes. ICLR.
[3] Liang, Y., & Li, W. (2022). Optimizing Class Distribution in Memory for Multi-Label Online Continual Learning. ArXiv, abs/2209.11469.
[4] Du, K., Lyu, F., Li, L., Hu, F., Feng, W., Xu, F., Xi, X., & Cheng, H. (2022). Multi-Label Continual Learning using Augmented Graph Convolutional Network. ArXiv, abs/2211.14763.