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Register a new userReduNet: A White-box Deep Network from the Principle of Maximizing Rate Reduction
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Added by
Yaodong Yu
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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This work attempts to provide a plausible theoretical framework that aims to interpret modern deep (convolutional) networks from the principles of data compression and discriminative representation. We argue that for high-dimensional multi-class data, the optimal linear discriminative representation maximizes the coding rate difference between the whole dataset and the average of all the subsets. We show that the basic iterative gradient ascent scheme for optimizing the rate reduction objective naturally leads to a multi-layer deep network, named ReduNet, which shares common characteristics of modern deep networks. The deep layered architectures, linear and nonlinear operators, and even parameters of the network are all explicitly constructed layer-by-layer via forward propagation, although they are amenable to fine-tuning via back propagation. All components of so-obtained ``white-box network have precise optimization, statistical, and geometric interpretation. Moreover, all linear operators of the so-derived network naturally become multi-channel convolutions when we enforce classification to be rigorously shift-invariant. The derivation in the invariant setting suggests a trade-off between sparsity and invariance, and also indicates that such a deep convolution network is significantly more efficient to construct and learn in the spectral domain. Our preliminary simulations and experiments clearly verify the effectiveness of both the rate reduction objective and the associated ReduNet. All code and data are available at https://github.com/Ma-Lab-Berkeley.
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To learn intrinsic low-dimensional structures from high-dimensional data that most discriminate between classes, we propose the principle of Maximal Coding Rate Reduction ($text{MCR}^2$), an information-theoretic measure that maximizes the coding rate difference between the whole dataset and the sum of each individual class. We clarify its relationships with most existing frameworks such as cross-entropy, information bottleneck, information gain, contractive and contrastive learning, and provide theoretical guarantees for learning diverse and discriminative features. The coding rate can be accurately computed from finite samples of degenerate subspace-like distributions and can learn intrinsic representations in supervised, self-supervised, and unsupervised settings in a unified manner. Empirically, the representations learned using this principle alone are significantly more robust to label corruptions in classification than those using cross-entropy, and can lead to state-of-the-art results in clustering mixed data from self-learned invariant features.
This work attempts to interpret modern deep (convolutional) networks from the principles of rate reduction and (shift) invariant classification. We show that the basic iterative gradient ascent scheme for optimizing the rate reduction of learned features naturally leads to a multi-layer deep network, one iteration per layer. The layered architectures, linear and nonlinear operators, and even parameters of the network are all explicitly constructed layer-by-layer in a forward propagation fashion by emulating the gradient scheme. All components of this white box network have precise optimization, statistical, and geometric interpretation. This principled framework also reveals and justifies the role of multi-channel lifting and sparse coding in early stage of deep networks. Moreover, all linear operators of the so-derived network naturally become multi-channel convolutions when we enforce classification to be rigorously shift-invariant. The derivation also indicates that such a convolutional network is significantly more efficient to construct and learn in the spectral domain. Our preliminary simulations and experiments indicate that so constructed deep network can already learn a good discriminative representation even without any back propagation training.
While there exist a plethora of deep learning tools and frameworks, the fast-growing complexity of the field brings new demands and challenges, such as more flexible network design, speedy computation on distributed setting, and compatibility between different tools. In this paper, we introduce Neural Network Libraries (https://nnabla.org), a deep learning framework designed from engineers perspective, with emphasis on usability and compatibility as its core design principles. We elaborate on each of our design principles and its merits, and validate our attempts via experiments.
Manifold learning-based encoders have been playing important roles in nonlinear dimensionality reduction (NLDR) for data exploration. However, existing methods can often fail to preserve geometric, topological and/or distributional structures of data. In this paper, we propose a deep manifold learning framework, called deep manifold transformation (DMT) for unsupervised NLDR and embedding learning. DMT enhances deep neural networks by using cross-layer local geometry-preserving (LGP) constraints. The LGP constraints constitute the loss for deep manifold learning and serve as geometric regularizers for NLDR network training. Extensive experiments on synthetic and real-world data demonstrate that DMT networks outperform existing leading manifold-based NLDR methods in terms of preserving the structures of data.
Photoplethysmogram (PPG) is increasingly used to provide monitoring of the cardiovascular system under ambulatory conditions. Wearable devices like smartwatches use PPG to allow long term unobtrusive monitoring of heart rate in free living conditions. PPG based heart rate measurement is unfortunately highly susceptible to motion artifacts, particularly when measured from the wrist. Traditional machine learning and deep learning approaches rely on tri-axial accelerometer data along with PPG to perform heart rate estimation. The conventional learning based approaches have not addressed the need for device-specific modeling due to differences in hardware design among PPG devices. In this paper, we propose a novel end to end deep learning model to perform heart rate estimation using 8 second length input PPG signal. We evaluate the proposed model on the IEEE SPC 2015 dataset, achieving a mean absolute error of 3.36+-4.1BPM for HR estimation on 12 subjects without requiring patient specific training. We also studied the feasibility of applying transfer learning along with sparse retraining from a comprehensive in house PPG dataset for heart rate estimation across PPG devices with different hardware design.
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