A Kernel Perspective for Regularizing Deep Neural Networks

We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various practical strategies. Specifically, this perspective (i) provides a common umbrella for many existing regularization principles, including spectral norm and gradient penalties, or adversarial training, (ii) leads to new effective regularization penalties, and (iii) suggests hybrid strategies combining lower and upper bounds to get better approximations of the RKHS norm. We experimentally show this approach to be effective when learning on small datasets, or to obtain adversarially robust models.Comment: ICM

Convolutional Kernel Networks for Graph-Structured Data

We introduce a family of multilayer graph kernels and establish new links between graph convolutional neural networks and kernel methods. Our approach generalizes convolutional kernel networks to graph-structured data, by representing graphs as a sequence of kernel feature maps, where each node carries information about local graph substructures. On the one hand, the kernel point of view offers an unsupervised, expressive, and easy-to-regularize data representation, which is useful when limited samples are available. On the other hand, our model can also be trained end-to-end on large-scale data, leading to new types of graph convolutional neural networks. We show that our method achieves competitive performance on several graph classification benchmarks, while offering simple model interpretation. Our code is freely available at https://github.com/claying/GCKN

A Trainable Optimal Transport Embedding for Feature Aggregation and its Relationship to Attention

We address the problem of learning on sets of features, motivated by the need of performing pooling operations in long biological sequences of varying sizes, with long-range dependencies, and possibly few labeled data. To address this challenging task, we introduce a parametrized representation of fixed size, which embeds and then aggregates elements from a given input set according to the optimal transport plan between the set and a trainable reference. Our approach scales to large datasets and allows end-to-end training of the reference, while also providing a simple unsupervised learning mechanism with small computational cost. Our aggregation technique admits two useful interpretations: it may be seen as a mechanism related to attention layers in neural networks, or it may be seen as a scalable surrogate of a classical optimal transport-based kernel. We experimentally demonstrate the effectiveness of our approach on biological sequences, achieving state-of-the-art results for protein fold recognition and detection of chromatin profiles tasks, and, as a proof of concept, we show promising results for processing natural language sequences. We provide an open-source implementation of our embedding that can be used alone or as a module in larger learning models at https://github.com/claying/OTK.Comment: ICLR 202

GraphiT: Encoding Graph Structure in Transformers

We show that viewing graphs as sets of node features and incorporating structural and positional information into a transformer architecture is able to outperform representations learned with classical graph neural networks (GNNs). Our model, GraphiT, encodes such information by (i) leveraging relative positional encoding strategies in self-attention scores based on positive definite kernels on graphs, and (ii) enumerating and encoding local sub-structures such as paths of short length. We thoroughly evaluate these two ideas on many classification and regression tasks, demonstrating the effectiveness of each of them independently, as well as their combination. In addition to performing well on standard benchmarks, our model also admits natural visualization mechanisms for interpreting graph motifs explaining the predictions, making it a potentially strong candidate for scientific applications where interpretation is important. Code available at https://github.com/inria-thoth/GraphiT

Convolutional Kernel Networks for Graph-Structured Data

International audienceWe introduce a family of multilayer graph kernels and establish new links between graph convolutional neural networks and kernel methods. Our approach generalizes convolutional kernel networks to graph-structured data, by representing graphs as a sequence of kernel feature maps, where each node carries information about local graph substructures. On the one hand, the kernel point of view offers an unsupervised, expressive, and easy-to-regularize data representation, which is useful when limited samples are available. On the other hand, our model can also be trained end-to-end on large-scale data, leading to new types of graph convolutional neural networks. We show that our method achieves competitive performance on several graph classification benchmarks, while offering simple model interpretation. Our code is freely available at https://github.com/claying/GCKN

Biological Sequence Modeling with Convolutional Kernel Networks

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Recurrent Kernel Networks

International audienceSubstring kernels are classical tools for representing biological sequences or text.However, when large amounts of annotated data are available, models that allowend-to-end training such as neural networks are often preferred. Links betweenrecurrent neural networks (RNNs) and substring kernels have recently been drawn,by formally showing that RNNs with specific activation functions were pointsin a reproducing kernel Hilbert space (RKHS). In this paper, we revisit this linkby generalizing convolutional kernel networks—originally related to a relaxationof the mismatch kernel—to model gaps in sequences. It results in a new type ofrecurrent neural network which can be trained end-to-end with backpropagation, orwithout supervision by using kernel approximation techniques. We experimentallyshow that our approach is well suited to biological sequences, where it outperformsexisting methods for protein classification tasks

A Trainable Optimal Transport Embedding for Feature Aggregation and its Relationship to Attention

International audienceWe address the problem of learning on sets of features, motivated by the need of performing pooling operations in long biological sequences of varying sizes, with long-range dependencies, and possibly few labeled data. To address this challenging task, we introduce a parametrized representation of fixed size, which embeds and then aggregates elements from a given input set according to the optimal transport plan between the set and a trainable reference. Our approach scales to large datasets and allows end-to-end training of the reference, while also providing a simple unsupervised learning mechanism with small computational cost. Our aggregation technique admits two useful interpretations: it may be seen as a mechanism related to attention layers in neural networks, or it may be seen as a scalable surrogate of a classical optimal transport-based kernel. We experimentally demonstrate the effectiveness of our approach on biological sequences, achieving state-of-the-art results for protein fold recognition and detection of chromatin profiles tasks, and, as a proof of concept, we show promising results for processing natural language sequences. We provide an open-source implementation of our embedding that can be used alone or as a module in larger learning models at https://github.com/claying/OTK