This is the distribution over datasets one obtains by first sampling a task t from Pt, and then sampling a dataset S from Pmz|t. Here p(S) corresponds to the marginal distribution over datasets S. Note that the last line above holds because E P f(,S) does not depend on t. Thus, in this section, we present a specialization of the bound for Gaussian distributions. Let P have mean µ and covariance; thus P = N(µ,) and analogously P,0 = N(µ0, 0). We can then apply the analytical form for the KL-divergence between two multivariate Gaussian distributions to the bound presented in Theorem 3. The result is the following bound holding under the same assumptions as Theorem 3: L(P,Pt) 1 l We implement the above bound in code instead of the non-specialized form of the KL divergence to speed up computations and simplify gradient computations. A.3.2 Few-Shot Learning Bound with Validation Data In this section, we will assume that, in addition to the training data S Pmz|t, we have access to validation data Sva Pnz|t at meta-training time. We will show that a meta-learning generalization bound can still be obtained in this case.

We introduce an efficient optimization-based meta-learning technique for large-scale neural field training by realizing significant memory savings through automated online context point selection.

The meta generator is termed as MGDD in our approach. Once adapted, it can handle arbitrary sizes of synthetic datasets, even for those unseen during adaptation.

Zero-shot learning (ZSL) tackles the unseen class recognition problem, transferring semantic knowledge from seen classes to unseen ones. Typically, to guarantee desirable knowledge transfer, a common (latent) space is adopted for associating the visual and semantic domains in ZSL. However, existing common space learning methods align the semantic and visual domains by merely mitigating distribution disagreement through one-step adaptation. This strategy is usually ineffective due to the heterogeneous nature of the feature representations in the two domains, which intrinsically contain both distribution and structure variations. To address this and advance ZSL, we propose a novel hierarchical semantic-visual adaptation (HSVA) framework.

Inspired by the concept of preconditioning, we propose a novel method to increase adaptation speed for gradient-based meta-learning methods without incurring extra parameters. We demonstrate that recasting the optimisation problem to a non-linear least-squares formulation provides a principled way to actively enforce a well-conditioned parameter space for meta-learning models based on the concepts of the condition number and local curvature. Our comprehensive evaluations show that the proposed method significantly outperforms its unconstrained counterpart especially during initial adaptation steps, while achieving comparable or better overall results on several few-shot classification tasks - creating the possibility of dynamically choosing the number of adaptation steps at inference time.

Rapidly learning abstract concepts from limited examples is a hallmark of human intelligence. This work investigates whether gradient-based meta-learning can equip neural networks with inductive biases for efficient few-shot acquisition of discrete concepts. I compare meta-learning methods against a supervised learning baseline on Boolean concepts (logical statements) generated by a probabilistic context-free grammar (PCFG). By systematically varying concept dimensionality (number of features) and recursive compositionality (depth of grammar recursion), I delineate between complexity regimes in which meta-learning robustly improves few-shot concept learning and regimes in which it does not. Meta-learners are much better able to handle compositional complexity than featural complexity. I highlight some reasons for this with a representational analysis of the weights of meta-learners and a loss landscape analysis demonstrating how featural complexity increases the roughness of loss trajectories, allowing curvature-aware optimization to be more effective than first-order methods. I find improvements in out-of-distribution generalization on complex concepts by increasing the number of adaptation steps in meta-SGD, where adaptation acts as a way of encouraging exploration of rougher loss basins. Overall, this work highlights the intricacies of learning compositional versus featural complexity in high dimensional concept spaces and provides a road to understanding the role of 2nd order methods and extended gradient adaptation in few-shot concept learning.