> For the complete documentation index, see [llms.txt](https://lichangbin.gitbook.io/paper_notes/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://lichangbin.gitbook.io/paper_notes/modular-meta-learning.md). # Modular Meta Learning ## Motivation Previous approaches to meta-learning have focused on finding distributions or initial values of parameters. Our objective is similar, but rather than focusing on transferring information about parameter values, we focus on finding a set of reusable modules that can form components of a solution to a new task, possibly with a small amount of tuning. The authors provide an algorithm, called **BounceGrad**, which learns a set of modules and then combines them appropriately for a new task. ## Objective Given the specification of a composition rule and a basis set of modules, $$(\mathcal{C}, F,\mathbb{\Theta})$$represents a set of possible functional input-output mappings that will serve as the hypothesis space for the meta-test task. $$F$$ is a basis set of modules, which are functions $$f\_1,f\_2,\dots,f\_k$$ Each function has a parametric form $$y=f\_i(x;\theta\_i)$$where $$\theta\_i$$is a fixed-dimensional vector of parameters. In this work, all the $$f\_i$$are neural networks, potentially with different architectures, and the parameters $$\Theta=(\theta\_1,\dots,\theta\_k)$$ are the weights of the neural networks, which differ among the modules.\ \ Some examples of modules: * Single module $$h(x)=f\_i(x)$$ * A fixed compositional structure: $$h(x)=f\_i(x)+f\_j(x)$$ * A weighted ensemble. ![Objective Function in the paper](/files/-MGaV52wYfZhiFpr4ZE4) $$\mathbb{S}$$: the set of possible structures and $$S\in \mathbb{S}$$ is a particular structure generated by $$\mathcal{C}$$ .\ This approach has two phases: an **off-line meta-learning phase** and an **on-line meta-test learning phase**. **Meta-learning phase:** we take training and validation data sets for tasks $$1, \dots,k$$ as input and generate a parametrization $$\mathbb{\Theta}$$for each module. The objective is to construct modules that will work together as good building blocks for future tasks. At meta-learning time, $$S$$ is specified, and the objective is to find parameter values $$\mathbb{\Theta}$$ that constitute a set of modules that can be recombined to effectively solve each of the training tasks. Validation set is used for the meta-training tasks to avoid choosing $$\mathbb{\Theta}$$ in a way that overfits. The training objective is to find $$\mathbb{\Theta}$$that minimizing the average generalization performance of the hypotheses $$S\_{\Theta}^{\*}$$using parameter set $$\Theta$$ : (See above figure)
**Meta-test learning phase:** we take a training data set for the meta-test task as input, as well as $$\mathbb{S}$$ and $$\mathbb{\Theta}$$; the output is a compositional form $$S\in \mathbb{S}$$which includes a selection of modules $$f\_1,\dots,f\_m$$ to be used in that form. Since$$\mathbb{\Theta}$$is already specified, the choice of $$S$$ completely determines a mapping from inputs to outputs.
It looks that this is a bi-level optimization problem, and use iterative optimization method to solve it. **Notes**: * Simulated Annealing * iteration optimization vs bilevel optimization ## Reference * * * h[ttps://phillipi.github.io/6.882/2020/notes/The%20problem%20of%20very%20little%20data/Modular%20Meta-Learning.pdf](https://phillipi.github.io/6.882/2020/notes/The%20problem%20of%20very%20little%20data/Modular%20Meta-Learning.pdf) * * *