This paper introduces a hypothesis space for deep learning based on deep neural networks (DNNs). By treating a DNN as a function of two variables - the input variable and the parameter variable - we consider the set of DNNs where the parameter variable belongs to a space of weight matrices and biases determined by a prescribed depth and layer widths. To construct a Banach space of functions of the input variable, we take the weak* closure of the linear span of this DNN set. We prove that the resulting Banach space is a reproducing kernel Banach space (RKBS) and explicitly construct its reproducing kernel. Furthermore, we investigate two learning models - regularized learning and the minimum norm interpolation (MNI) problem - within the RKBS framework by establishing representer theorems. These theorems reveal that the solutions to these learning problems can be expressed as a finite sum of kernel expansions based on training data.
Collaborative Robotics and Intelligent Systems (CoRIS) Institute（协作机器人与智能系统研究所）；Oregon State University（俄勒冈州立大学）
In many object recognition applications, the set of possible categories is an open set, and the deployed recognition system will encounter novel objects belonging to categories unseen during training. Detecting such "novel category" objects is usually formulated as an anomaly detection problem. Anomaly detection algorithms for feature-vector data identify anomalies as outliers, but outlier detection has not worked well in deep learning. Instead, methods based on the computed logits of visual object classifiers give state-of-the-art performance. This paper proposes the Familiarity Hypothesis th…
Deep reinforcement learning (DRL) is capable of learning high-performing policies on a variety of complex high-dimensional tasks, ranging from video games to robotic manipulation. However, standard DRL methods often suffer from poor sample efficiency, partially because they aim to be entirely problem-agnostic. In this work, we introduce a novel approach to exploration and hierarchical skill learning that derives its sample efficiency from intuitive assumptions it makes about the behavior of objects both in the physical world and simulations which mimic physics. Specifically, we propose the Hyp…
We show that the number of unique function mappings in a neural network hypothesis space is inversely proportional to $\prod_lU_l!$, where $U_{l}$ is the number of neurons in the hidden layer $l$.
Selecting appropriate regularization coefficients is critical to performance with respect to regularized empirical risk minimization problems. Existing theoretical approaches attempt to determine the coefficients in order for regularized empirical objectives to be upper-bounds of true objectives, uniformly over a hypothesis space. Such an approach is, however, known to be over-conservative, especially in high-dimensional settings with large hypothesis space. In fact, an existing generalization error bound in variance-based regularization is $O(\sqrt{d \log n/n})$, where $d$ is the dimension of…
Due to a resource-constrained environment, network compression has become an important part of deep neural networks research. In this paper, we propose a new compression method, \textit{Inter-Layer Weight Prediction} (ILWP) and quantization method which quantize the predicted residuals between the weights in all convolution layers based on an inter-frame prediction method in conventional video coding schemes. Furthermore, we found a phenomenon \textit{Smoothly Varying Weight Hypothesis} (SVWH) which is that the weights in adjacent convolution layers share strong similarity in shapes and values…
University of Vienna（维也纳大学）；ETH Zürich（苏黎世联邦理工学院）；University of Münster（明斯特大学）
The development of new classification and regression algorithms based on empirical risk minimization (ERM) over deep neural network hypothesis classes, coined deep learning, revolutionized the area of artificial intelligence, machine learning, and data analysis. In particular, these methods have been applied to the numerical solution of high-dimensional partial differential equations with great success. Recent simulations indicate that deep learning-based algorithms are capable of overcoming the curse of dimensionality for the numerical solution of Kolmogorov equations, which are widely used i…
Hypothesis Testing and Machine Learning: Interpreting Variable Effects in Deep Artificial Neural Networks using Cohen's f2
University of South Carolina（南卡罗来纳大学）；University of Kassel（卡塞尔大学）；University of Wales（威尔士大学）；Technical University Munich（慕尼黑工业大学）；University of Newcastle upon Tyne（纽卡斯尔大学）；Università per Stranieri di Perugia（佩鲁贾外国人大学）
McGill University（麦吉尔大学）；Mila；Microsoft Research Montréal（微软研究院蒙特利尔）；Université de Montréal（蒙特利尔大学）
We begin with the hypothesis that a model-free agent whose representations are predictive of properties of future states (beyond expected rewards) will be more capable of solving and adapting to new RL problems. To test that hypothesis, we introduce an objective based on Deep InfoMax (DIM) which trains the agent to predict the future by maximizing the mutual information between its internal representation of successive timesteps. We test our approach in several synthetic settings, where it successfully learns representations that are predictive of the future. Finally, we augment C51, a strong …
A fascinating hypothesis is that human and animal intelligence could be explained by a few principles (rather than an encyclopedic list of heuristics). If that hypothesis was correct, we could more easily both understand our own intelligence and build intelligent machines. Just like in physics, the principles themselves would not be sufficient to predict the behavior of complex systems like brains, and substantial computation might be needed to simulate human-like intelligence. This hypothesis would suggest that studying the kind of inductive biases that humans and animals exploit could help b…
Pompeu Fabra University（庞培法布拉大学）；ICREA（加泰罗尼亚高等研究院）；Barcelona Graduate School of Economics（巴塞罗那经济研究生院）；Universitat Pompeu Fabra（庞培法布拉大学）
We introduce a notion of algorithmic stability of learning algorithms---that we term \emph{argument stability}---that captures stability of the hypothesis output by the learning algorithm in the normed space of functions from which hypotheses are selected. The main result of the paper bounds the generalization error of any learning algorithm in terms of its argument stability. The bounds are based on martingale inequalities in the Banach space to which the hypotheses belong. We apply the general bounds to bound the performance of some learning algorithms based on empirical risk minimization an…
Human input has enabled autonomous systems to improve their capabilities and achieve complex behaviors that are otherwise challenging to generate automatically. Recent work focuses on how robots can use such input - like demonstrations or corrections - to learn intended objectives. These techniques assume that the human's desired objective already exists within the robot's hypothesis space. In reality, this assumption is often inaccurate: there will always be situations where the person might care about aspects of the task that the robot does not know about. Without this knowledge, the robot c…
Obtaining reliable, adaptive confidence sets for prediction functions (hypotheses) is a central challenge in sequential decision-making tasks, such as bandits and model-based reinforcement learning. These confidence sets typically rely on prior assumptions on the hypothesis space, e.g., the known kernel of a Reproducing Kernel Hilbert Space (RKHS). Hand-designing such kernels is error prone, and misspecification may lead to poor or unsafe performance. In this work, we propose to meta-learn a kernel from offline data (Meta-KeL). For the case where the unknown kernel is a combination of known ba…
In this paper we investigate two hypothesis regarding the use of deep reinforcement learning in multiple tasks. The first hypothesis is driven by the question of whether a deep reinforcement learning algorithm, trained on two similar tasks, is able to outperform two single-task, individually trained algorithms, by more efficiently learning a new, similar task, that none of the three algorithms has encountered before. The second hypothesis is driven by the question of whether the same multi-task deep RL algorithm, trained on two similar tasks and augmented with elastic weight consolidation (EWC…
