Training deep learning models from a stream of nonstationary data is a critical problem to be solved to achieve general artificial intelligence. As a promising solution, the continual learning (CL) technique aims to build intelligent systems that have the plasticity to learn from new information without forgetting the previously obtained knowledge. Unfortunately, existing CL methods face two nontrivial limitations. First, when updating a model with new data, existing CL methods usually constrain the model parameters within the vicinity of the parameters optimized for old data, limiting the exploration ability of the model; second, the important strength of each parameter (used to consolidate the previously learned knowledge) is fixed and thus is suboptimal for the dynamic parameter updates. To address these limitations, we first relax the vicinity constraints with a global definition of the important strength, which allows us to explore the full parameter space. Specifically, we define the important strength as the sensitivity of the global loss function to the model parameters. Moreover, we propose adjusting the important strength adaptively to align it with the dynamic parameter updates. Through extensive experiments on popular data sets, we demonstrate that our proposed method outperforms the strong baselines by up to 24% in terms of average accuracy.

Data samples collected for training machine learning models are typically assumed to be independent and identically distributed (i.i.d.). Recent research has demonstrated that this assumption can be problematic as it simplifies the manifold of structured data. This has motivated different research areas such as data poisoning, model improvement, and explanation of machine learning models. In this work, we study the influence of a sample on determining the intrinsic topological features of its underlying manifold. We propose the Shapley homology framework, which provides a quantitative metric for the influence of a sample of the homology of a simplicial complex. Our proposed framework consists of two main parts: homology analysis, where we compute the Betti number of the target topological space, and Shapley value calculation, where we decompose the topological features of a complex built from data points to individual points. By interpreting the influence as a probability measure, we further define an entropy that reflects the complexity of the data manifold. Furthermore, we provide a preliminary discussion of the connection of the Shapley homology to the Vapnik-Chervonenkis dimension. Empirical studies show that when the zero-dimensional Shapley homology is used on neighboring graphs, samples with higher influence scores have a greater impact on the accuracy of neural networks that determine graph connectivity and on several regular grammars whose higher entropy values imply greater difficulty in being learned.

Rule extraction from black box models is critical in domains that require model validation before implementation, as can be the case in credit scoring and medical diagnosis. Though already a challenging problem in statistical learning in general, the difficulty is even greater when highly nonlinear, recursive models, such as recurrent neural networks (RNNs), are fit to data. Here, we study the extraction of rules from second-order RNNs trained to recognize the Tomita grammars. We show that production rules can be stably extracted from trained RNNs and that in certain cases, the rules outperform the trained RNNs.