We present novel graph kernels for graphs with node and edge labels that have ordered neighborhoods, i.e. when neighbor nodes followanorder.

Several papers consider approaches that limit the number of bits to represent floating point numbers [13, 24, 31]. Recent work proposes adaptive tuning of the compression ratio [7].

Algorithm Thei Requirinitialx0,i, 1: forj =0 ,1,2,..., 1do 2: Randomlymtraining 3: Compute 4: Update 5: if((j+ 1)p)=0 then 6: Compute 7: Quantize 8: Av 9: Update 10: end 11: end Inthe achie O(1/ p MK)con limited impair gradient 2-bit ratio 32/2 =(if We the communicate issho each parameters.

The bottom graph is a historical example ofunfairness: evenifthere would benobias betweenLoanand Race,redlining(i.e. the practice of refusing aloan topeople living in certain areas) would discriminate indirectly based on race [1,2,3,4]. This example also showswhysimply removing or not measuring a sensitive attribute does not suffice: not only does this ignore indirect bias, but hiding the protected attribute leads to an (additional) correlation betweenPostcodeandLoandue to confounding. InTable 1, we observethat naively removing the protected attribute only ensures FTU fairness, asshown by: GAN-PR, WGAN-GP-PR, and DECAF-PR. This is the direct result of the construction of generatorG and follows a similar argument asProposition 2of[6]. P(Xi|{Xj:(Xj Xi) E}) Given each Gi (see Eq. 2 paper) has enough capacity,G can thus express the full distribution PX(X).

The Power Descent, defined for allα = 1, is one such algorithm and we establish in our work the full proof ofits convergence towards the optimal mixture weights whenα < 1.

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Existing graph embedding models often have weaknesses in exploiting graph structure similarities, potential dependencies among nodes and global network properties. To this end, we present U2GAN, a novel unsupervised model leveraging on the strength of the recently introduced universal self-attention network (Dehghani et al., 2019), to learn low-dimensional embeddings of graphs which can be used for graph classification. In particular, given an input graph, U2GAN first applies a self-attention computation, which is then followed by a recurrent transition to iteratively memorize its attention on vector representations of each node and its neighbors across each iteration. Thus, U2GAN can address the weaknesses in the existing models in order to produce plausible node embeddings whose sum is the final embedding of the whole graph. Experimental results show that our unsupervised U2GAN produces new state-of-the-art performances on a range of well-known benchmark datasets for the graph classification task. It even outperforms supervised methods in most of benchmark cases.

Recently, the Weisfeiler-Lehman (WL) graph isomorphism test was used to measure the expressive power of graph neural networks (GNN). It was shown that the popular message passing GNN cannot distinguish between graphs that are indistinguishable by the 1-WL test (Morris et al. 2018; Xu et al. 2019). Unfortunately, many simple instances of graphs are indistinguishable by the 1-WL test. In search for more expressive graph learning models we build upon the recent k-order invariant and equivariant graph neural networks (Maron et al. 2019a,b) and present two results: First, we show that such k-order networks can distinguish between non-isomorphic graphs as good as the k-WL tests, which are provably stronger than the 1-WL test for k>2. This makes these models strictly stronger than message passing models. Unfortunately, the higher expressiveness of these models comes with a computational cost of processing high order tensors. Second, setting our goal at building a provably stronger, simple and scalable model we show that a reduced 2-order network containing just scaled identity operator, augmented with a single quadratic operation (matrix multiplication) has a provable 3-WL expressive power. Differently put, we suggest a simple model that interleaves applications of standard Multilayer-Perceptron (MLP) applied to the feature dimension and matrix multiplication. We validate this model by presenting state of the art results on popular graph classification and regression tasks. To the best of our knowledge, this is the first practical invariant/equivariant model with guaranteed 3-WL expressiveness, strictly stronger than message passing models.

Invento CEO Balaji Vishwanathan (right) and an employee interact with Spod, next to MITRI, a humanoid developed by the firm. At an office in HSR Layout, a box-shaped robot, mounted with a tablet, moves along the office floor while avoiding objects. As it detects a human face, it stops to greet and introduce itself: "Greetings, I'm Spod. I'm here to help you shop." Spod is an artificial intelligence-enabled robotic shopping assistant that visitors to supermarkets may well see in near future.

The task of representing entire graphs has seen a surge of prominent results, mainly due to learning convolutional neural networks (CNNs) on graph-structured data. While CNNs demonstrate state-of-the-art performance in graph classification task, such methods are supervised and therefore steer away from the original problem of network representation in task-agnostic manner. Here, we coherently propose an approach for embedding entire graphs and show that our feature representations with SVM classifier increase classification accuracy of CNN algorithms and traditional graph kernels. For this we describe a recently discovered graph object, anonymous walk, on which we design task-independent algorithms for learning graph representations in explicit and distributed way. Overall, our work represents a new scalable unsupervised learning of state-of-the-art representations of entire graphs.