In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Example Input: Domain adaptation addresses the common problem when the target distribution generating our test data drifts from the source (training) distribution. While absent assumptions, domain adaptation is impossible, strict conditions, e.g. covariate or label shift, enable principled algorithms. Recently-proposed domain-adversarial approaches consist of aligning source and target encodings, often motivating this approach as minimizing two (of three) terms in a theoretical bound on target error. Unfortunately, this minimization can cause arbitrary increases in the third term, e.g. they can break down under shifting label distributions. We propose asymmetrically-relaxed distribution alignment, a new approach that overcomes some limitations of standard domain-adversarial algorithms. Moreover, we characterize precise assumptions under which our algorithm is theoretically principled and demonstrate empirical benefits on both synthetic and real datasets.
Example Output: Instead of strict distribution alignments in traditional deep domain adaptation objectives, which fails when target label distribution shifts, we propose to optimize a relaxed objective with new analysis, new algorithms, and experimental validation.

Example Input: We propose and study a method for learning interpretable representations for the task of regression. Features are represented as networks of multi-type expression trees comprised of activation functions common in neural networks in addition to other elementary functions. Differentiable features are trained via gradient descent, and the performance of features in a linear model is used to weight the rate of change among subcomponents of each representation. The search process maintains an archive of representations with accuracy-complexity trade-offs to assist in generalization and interpretation. We compare several stochastic optimization approaches within this framework. We benchmark these variants on 100 open-source regression problems in comparison to state-of-the-art machine learning approaches. Our main finding is that this approach produces the highest average test scores across problems while producing representations that are orders of magnitude smaller than the next best performing method (gradient boosting). We also report a negative result in which attempts to directly optimize the disentanglement of the representation result in more highly correlated features.
Example Output: Representing the network architecture as a set of syntax trees and optimizing their structure leads to accurate and concise regression models. 

Example Input: The joint optimization of representation learning and clustering in the embedding space has experienced a breakthrough in recent years. In spite of the advance, clustering with representation learning has been limited to flat-level categories, which oftentimes involves cohesive clustering with a focus on instance relations. To overcome the limitations of flat clustering, we introduce hierarchically clustered representation learning (HCRL), which simultaneously optimizes representation learning and hierarchical clustering in the embedding space. Specifically, we place a nonparametric Bayesian prior on embeddings to handle dynamic mixture hierarchies under the variational autoencoder framework, and to adopt the generative process of a hierarchical-versioned Gaussian mixture model. Compared with a few prior works focusing on unifying representation learning and hierarchical clustering, HCRL is the first model to consider a generation of deep embeddings from every component of the hierarchy, not just leaf components. This generation process enables more meaningful separations and mergers of clusters via branches in a hierarchy. In addition to obtaining hierarchically clustered embeddings, we can reconstruct data by the various abstraction levels, infer the intrinsic hierarchical structure, and learn the level-proportion features. We conducted evaluations with image and text domains, and our quantitative analyses showed competent likelihoods and the best accuracies compared with the baselines.
Example Output:
We introduce hierarchically clustered representation learning (HCRL), which simultaneously optimizes representation learning and hierarchical clustering in the embedding space.