Although model-agnostic meta-learning (MAML) is a very successful algorithm in meta-learning practice, it can have high computational cost because it updates all model parameters over both the inner loop of task-specific adaptation and the outer-loop of meta initialization training. A more efficient algorithm ANIL (which refers to almost no inner loop) was proposed recently by Raghu et al. 2019, which adapts only a small subset of parameters in the inner loop and thus has substantially less computational cost than MAML as demonstrated by extensive experiments. However, the theoretical convergence of ANIL has not been studied yet. In this paper, we characterize the convergence rate and the computational complexity for ANIL under two representative inner-loop loss geometries, i.e., strongly-convexity and nonconvexity. Our results show that such a geometric property can significantly affect the overall convergence performance of ANIL. For example, ANIL achieves a faster convergence rate for a strongly-convex inner-loop loss as the number $N$ of inner-loop gradient descent steps increases, but a slower convergence rate for a nonconvex inner-loop loss as $N$ increases. Moreover, our complexity analysis provides a theoretical quantification on the improved efficiency of ANIL over MAML.

Although model-agnostic meta-learning (MAML) is a very successful algorithm in meta-learning practice, it can have high computational cost because it updates all model parameters over both the inner loop of task-specific adaptation and the outer-loop of meta initialization training. A more efficient algorithm ANIL (which refers to almost no inner loop) was proposed recently by Raghu et al. 2019, which adapts only a small subset of parameters in the inner loop and thus has substantially less computational cost than MAML as demonstrated by extensive experiments. However, the theoretical convergence of ANIL has not been studied yet. In this paper, we characterize the convergence rate and the computational complexity for ANIL under two representative inner-loop loss geometries, i.e., strongly-convexity and nonconvexity. Our results show that such a geometric property can significantly affect the overall convergence performance of ANIL. For example, ANIL achieves a faster convergence rate for a strongly-convex inner-loop loss as the number N of inner-loop gradient descent steps increases, but a slower convergence rate for a nonconvex inner-loop loss as N increases.

Fine-tuning pre-trained transformers is a powerful technique for enhancing the performance of base models on specific tasks. From early applications in models like BERT to fine-tuning Large Language Models (LLMs), this approach has been instrumental in adapting general-purpose architectures for specialized downstream tasks. Understanding the fine-tuning process is crucial for uncovering how transformers adapt to specific objectives, retain general representations, and acquire task-specific features. This paper explores the underlying mechanisms of fine-tuning, specifically in the BERT transformer, by analyzing activation similarity, training Sparse AutoEncoders (SAEs), and visualizing token-level activations across different layers. Based on experiments conducted across multiple datasets and BERT layers, we observe a steady progression in how features adapt to the task at hand: early layers primarily retain general representations, middle layers act as a transition between general and task-specific features, and later layers fully specialize in task adaptation. These findings provide key insights into the inner workings of fine-tuning and its impact on representation learning within transformer architectures.

Weaknesses: - It is not very clear about the evaluation for outer iterations. Is the number of aggregated tasks affecting the convergence too? In MAML, the gradient for outer-loop is computed based on the inner-loop of several tasks. Particularly, the number of samples in the support set and the query set (on mini-ImageNet) may affect the error and the convergence. Fallah et al. [4] considers this number of samples in the inner-loop to their analysis.

This paper studies the convergence rate and computational complexity of ANIL (a variant of MAML) for cases of strongly-convex and nonconvex inner-loop loss. The paper focuses on an important problem (due to increasing interest in MAML type methods) and it empirically backups its theoretical claims. There were some concerns initially, specially those raised by R4 (providing no insight into improving the existing methods, discrepancy between optimization methods in theoretical analysis and empirical verification). However, authors' response was very helpful and at the end all reviewers agree that the submission is ready for publication. I strongly recommend authors' to incorporate R1's post rebuttal comment in the final version of this work, as it can be an important and yet easy to add component. I am referring to R1's request: " a simple theoretical example, such as a 1-dimensional quadratic objective, could elaborate on the tightness.

Although model-agnostic meta-learning (MAML) is a very successful algorithm in meta-learning practice, it can have high computational cost because it updates all model parameters over both the inner loop of task-specific adaptation and the outer-loop of meta initialization training. A more efficient algorithm ANIL (which refers to almost no inner loop) was proposed recently by Raghu et al. 2019, which adapts only a small subset of parameters in the inner loop and thus has substantially less computational cost than MAML as demonstrated by extensive experiments. However, the theoretical convergence of ANIL has not been studied yet. In this paper, we characterize the convergence rate and the computational complexity for ANIL under two representative inner-loop loss geometries, i.e., strongly-convexity and nonconvexity. Our results show that such a geometric property can significantly affect the overall convergence performance of ANIL. For example, ANIL achieves a faster convergence rate for a strongly-convex inner-loop loss as the number N of inner-loop gradient descent steps increases, but a slower convergence rate for a nonconvex inner-loop loss as N increases.

Recent advances in Federated Learning (FL) have paved the way towards the design of novel strategies for solving multiple learning tasks simultaneously, by leveraging cooperation among networked devices. Multi-Task Learning (MTL) exploits relevant commonalities across tasks to improve efficiency compared with traditional transfer learning approaches. By learning multiple tasks jointly, significant reduction in terms of energy footprints can be obtained. This article provides a first look into the energy costs of MTL processes driven by the Model-Agnostic Meta-Learning (MAML) paradigm and implemented in distributed wireless networks. The paper targets a clustered multi-task network setup where autonomous agents learn different but related tasks. The MTL process is carried out in two stages: the optimization of a meta-model that can be quickly adapted to learn new tasks, and a task-specific model adaptation stage where the learned meta-model is transferred to agents and tailored for a specific task. This work analyzes the main factors that influence the MTL energy balance by considering a multi-task Reinforcement Learning (RL) setup in a robotized environment. Results show that the MAML method can reduce the energy bill by at least 2 times compared with traditional approaches without inductive transfer. Moreover, it is shown that the optimal energy balance in wireless networks depends on uplink/downlink and sidelink communication efficiencies.