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Register a new userPolynomial Networks in Deep Classifiers
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Added by
Grigorios Chrysos
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Deep neural networks have been the driving force behind the success in classification tasks, e.g., object and audio recognition. Impressive results and generalization have been achieved by a variety of recently proposed architectures, the majority of which are seemingly disconnected. In this work, we cast the study of deep classifiers under a unifying framework. In particular, we express state-of-the-art architectures (e.g., residual and non-local networks) in the form of different degree polynomials of the input. Our framework provides insights on the inductive biases of each model and enables natural extensions building upon their polynomial nature. The efficacy of the proposed models is evaluated on standard image and audio classification benchmarks. The expressivity of the proposed models is highlighted both in terms of increased model performance as well as model compression. Lastly, the extensions allowed by this taxonomy showcase benefits in the presence of limited data and long-tailed data distributions. We expect this taxonomy to provide links between existing domain-specific architectures.
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Deep Convolutional Neural Networks (DCNNs) are currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful selection of their building blocks (e.g., residual blocks, rectifiers, sophisticated normalization schemes, to mention but a few). In this paper, we propose $Pi$-Nets, a new class of function approximators based on polynomial expansions. $Pi$-Nets are polynomial neural networks, i.e., the output is a high-order polynomial of the input. The unknown parameters, which are naturally represented by high-order tensors, are estimated through a collective tensor factorization with factors sharing. We introduce three tensor decompositions that significantly reduce the number of parameters and show how they can be efficiently implemented by hierarchical neural networks. We empirically demonstrate that $Pi$-Nets are very expressive and they even produce good results without the use of non-linear activation functions in a large battery of tasks and signals, i.e., images, graphs, and audio. When used in conjunction with activation functions, $Pi$-Nets produce state-of-the-art results in three challenging tasks, i.e. image generation, face verification and 3D mesh representation learning. The source code is available at url{https://github.com/grigorisg9gr/polynomial_nets}.
Deep Neural Networks (DNNs) are often criticized for being susceptible to adversarial attacks. Most successful defense strategies adopt adversarial training or random input transformations that typically require retraining or fine-tuning the model to achieve reasonable performance. In this work, our investigations of intermediate representations of a pre-trained DNN lead to an interesting discovery pointing to intrinsic robustness to adversarial attacks. We find that we can learn a generative classifier by statistically characterizing the neural response of an intermediate layer to clean training samples. The predictions of multiple such intermediate-layer based classifiers, when aggregated, show unexpected robustness to adversarial attacks. Specifically, we devise an ensemble of these generative classifiers that rank-aggregates their predictions via a Borda count-based consensus. Our proposed approach uses a subset of the clean training data and a pre-trained model, and yet is agnostic to network architectures or the adversarial attack generation method. We show extensive experiments to establish that our defense strategy achieves state-of-the-art performance on the ImageNet validation set.
Deep Convolutional Neural Networks (DCNNs) is currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful selection of their building blocks (e.g., residual blocks, rectifiers, sophisticated normalization schemes, to mention but a few). In this paper, we propose $Pi$-Nets, a new class of DCNNs. $Pi$-Nets are polynomial neural networks, i.e., the output is a high-order polynomial of the input. $Pi$-Nets can be implemented using special kind of skip connections and their parameters can be represented via high-order tensors. We empirically demonstrate that $Pi$-Nets have better representation power than standard DCNNs and they even produce good results without the use of non-linear activation functions in a large battery of tasks and signals, i.e., images, graphs, and audio. When used in conjunction with activation functions, $Pi$-Nets produce state-of-the-art results in challenging tasks, such as image generation. Lastly, our framework elucidates why recent generative models, such as StyleGAN, improve upon their predecessors, e.g., ProGAN.
One of the main factors that contributed to the large advances in autonomous driving is the advent of deep learning. For safer self-driving vehicles, one of the problems that has yet to be solved completely is lane detection. Since methods for this task have to work in real-time (+30 FPS), they not only have to be effective (i.e., have high accuracy) but they also have to be efficient (i.e., fast). In this work, we present a novel method for lane detection that uses as input an image from a forward-looking camera mounted in the vehicle and outputs polynomials representing each lane marking in the image, via deep polynomial regression. The proposed method is shown to be competitive with existing state-of-the-art methods in the TuSimple dataset while maintaining its efficiency (115 FPS). Additionally, extensive qualitative results on two additional public datasets are presented, alongside with limitations in the evaluation metrics used by recent works for lane detection. Finally, we provide source code and trained models that allow others to replicate all the results shown in this paper, which is surprisingly rare in state-of-the-art lane detection methods. The full source code and pretrained models are available at https://github.com/lucastabelini/PolyLaneNet.
We study deep neural networks with polynomial activations, particularly their expressive power. For a fixed architecture and activation degree, a polynomial neural network defines an algebraic map from weights to polynomials. The image of this map is the functional space associated to the network, and it is an irreducible algebraic variety upon taking closure. This paper proposes the dimension of this variety as a precise measure of the expressive power of polynomial neural networks. We obtain several theoretical results regarding this dimension as a function of architecture, including an exact formula for high activation degrees, as well as upper and lower bounds on layer widths in order for deep polynomials networks to fill the ambient functional space. We also present computational evidence that it is profitable in terms of expressiveness for layer widths to increase monotonically and then decrease monotonically. Finally, we link our study to favorable optimization properties when training weights, and we draw intriguing connections with tensor and polynomial decompositions.
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