This paper theoretically explains the intuition that simple concepts are more likely to be learned by deep neural networks (DNNs) than complex concepts. In fact, recent studies have observed [24, 15] and proved [26] the emergence of interactive concepts in a DNN, i.e., it is proven that a DNN usually only encodes a small number of interactive concepts, and can be considered to use their interaction effects to compute inference scores. Each interactive concept is encoded by the DNN to represent the collaboration between a set of input variables. Therefore, in this study, we aim to theoretically explain that interactive concepts involving more input variables (i.e., more complex concepts) are more difficult to learn. Our finding clarifies the exact conceptual complexity that boosts the learning difficulty.

Learning with neural networks relies on the complexity of their representable functions, but more importantly, their particular assignment of typical parameters to functions of different complexity. Taking the number of activation regions as a complexity measure, recent works have shown that the practical complexity of deep ReLU networks is often far from the theoretical maximum. In this work, we show that this phenomenon also occurs in networks with maxout (multi-argument) activation functions and when considering the decision boundaries in classification tasks. We also show that the parameter space has a multitude of full-dimensional regions with widely different complexity, and obtain nontrivial lower bounds on the expected complexity. Finally, we investigate different parameter initialization procedures and show that they can increase the speed of convergence in training.

Learning with neural networks relies on the complexity of their representable functions, but more importantly, their particular assignment of typical parameters to functions of different complexity. Taking the number of activation regions as a complexity measure, recent works have shown that the practical complexity of deep ReLU networks is often far from the theoretical maximum. In this work, we show that this phenomenon also occurs in networks with maxout (multi-argument) activation functions and when considering the decision boundaries in classification tasks. We also show that the parameter space has a multitude of full-dimensional regions with widely different complexity, and obtain nontrivial lower bounds on the expected complexity. Finally, we investigate different parameter initialization procedures and show that they can increase the speed of convergence in training.

This paper theoretically explains the intuition that simple concepts are more likely to be learned by deep neural networks (DNNs) than complex concepts. In fact, recent studies have observed [24, 15] and proved [26] the emergence of interactive concepts in a DNN, i.e., it is proven that a DNN usually only encodes a small number of interactive concepts, and can be considered to use their interaction effects to compute inference scores. Each interactive concept is encoded by the DNN to represent the collaboration between a set of input variables. Therefore, in this study, we aim to theoretically explain that interactive concepts involving more input variables (i.e., more complex concepts) are more difficult to learn. Our finding clarifies the exact conceptual complexity that boosts the learning difficulty.

Neural architecture search (NAS) aims to automate architecture design processes and improve the performance of deep neural networks. Platform-aware NAS methods consider both performance and complexity and can find well-performing architectures with low computational resources. Although ordinary NAS methods result in tremendous computational costs owing to the repetition of model training, one-shot NAS, which trains the weights of a supernetwork containing all candidate architectures only once during the search process, has been reported to result in a lower search cost. This study focuses on the architecture complexity-aware one-shot NAS that optimizes the objective function composed of the weighted sum of two metrics, such as the predictive performance and number of parameters. In existing methods, the architecture search process must be run multiple times with different coefficients of the weighted sum to obtain multiple architectures with different complexities. This study aims at reducing the search cost associated with finding multiple architectures. The proposed method uses multiple distributions to generate architectures with different complexities and updates each distribution using the samples obtained from multiple distributions based on importance sampling. The proposed method allows us to obtain multiple architectures with different complexities in a single architecture search, resulting in reducing the search cost. The proposed method is applied to the architecture search of convolutional neural networks on the CIAFR-10 and ImageNet datasets. Consequently, compared with baseline methods, the proposed method finds multiple architectures with varying complexities while requiring less computational effort.

Natural language question understanding has been one of the most important challenges in artificial intelligence. Indeed, eminent AI benchmarks such as the Turing test require an AI system to understand natural language questions, with various topics and complexity, and then respond appropriately. During the past few years, we have witnessed rapid progress in question answering technology, with virtual assistants like Siri, Google Now, and Cortana answering daily life questions, and IBM Watson winning over humans in Jeopardy!. Many questions the systems encounter are simple lookup questions (e.g., "Where is Chichen Itza?" or "Who's the manager of Man Utd?"). The answers can be found by searching the surface forms.