  In order to quickly adapt to new data, few-shot learning aims at learning
from few examples, often by using already acquired knowledge. The new data
often differs from the previously seen data due to a domain shift, that is, a
change of the input-target distribution. While several methods perform well on
small domain shifts like new target classes with similar inputs, larger domain
shifts are still challenging. Large domain shifts may result in high-level
concepts that are not shared between the original and the new domain, whereas
low-level concepts like edges in images might still be shared and useful. For
cross-domain few-shot learning, we suggest representation fusion to unify
different abstraction levels of a deep neural network into one representation.
We propose Cross-domain Hebbian Ensemble Few-shot learning (CHEF), which
achieves representation fusion by an ensemble of Hebbian learners acting on
different layers of a deep neural network. Ablation studies show that
representation fusion is a decisive factor to boost cross-domain few-shot
learning. On the few-shot datasets miniImagenet and tieredImagenet with small
domain shifts, CHEF is competitive with state-of-the-art methods. On
cross-domain few-shot benchmark challenges with larger domain shifts, CHEF
establishes novel state-of-the-art results in all categories. We further apply
CHEF on a real-world cross-domain application in drug discovery. We consider a
domain shift from bioactive molecules to environmental chemicals and drugs with
twelve associated toxicity prediction tasks. On these tasks, that are highly
relevant for computational drug discovery, CHEF significantly outperforms all
its competitors. Github: https://github.com/ml-jku/chef
