Recommendation Systems

A Graph Convolutional Network, or GCN, is an approach for semi-supervised learning on graph-structured data. It is based on an efficient variant of convolutional neural networks which operate directly on graphs. The choice of convolutional architecture is motivated via a localized first-order approximation of spectral graph convolutions. The model scales linearly in the number of graph edges and learns hidden layer representations that encode both local graph structure and features of nodes.

LightGCN is a type of graph convolutional neural network (GCN), including only the most essential component in GCN (neighborhood aggregation) for collaborative filtering. Specifically, LightGCN learns user and item embeddings by linearly propagating them on the user-item interaction graph, and uses the weighted sum of the embeddings learned at all layers as the final embedding.

The ARMA GNN layer implements a rational graph filter with a recursive approximation.

MetaFormer is a general architecture abstracted from Transformers by not specifying the token mixer.

Temporal Graph Network, or TGN, is a framework for deep learning on dynamic graphs represented as sequences of timed events. The memory (state) of the model at time $t$ consists of a vector $\mathbf{s}_i(t)$ for each node $i$ the model has seen so far. The memory of a node is updated after an event (e.g. interaction with another node or node-wise change), and its purpose is to represent the node's history in a compressed format. Thanks to this specific module, TGNs have the capability to memorize long term dependencies for each node in the graph. When a new node is encountered, its memory is initialized as the zero vector, and it is then updated for each event involving the node, even after the model has finished training.

MEI introduces the multi-partition embedding interaction technique with block term tensor format to systematically address the efficiency--expressiveness trade-off in knowledge graph embedding. It divides the embedding vector into multiple partitions and learns the local interaction patterns from data instead of using fixed special patterns as in ComplEx or SimplE models. This enables MEI to achieve optimal efficiency--expressiveness trade-off, not just being fully expressive. Previous methods such as TuckER, RESCAL, DistMult, ComplEx, and SimplE are suboptimal restricted special cases of MEI.

PoolFormer is instantiated from MetaFormer by specifying the token mixer as extremely simple operator, pooling. PoolFormer is utilized as a tool to verify MetaFormer hypothesis "MetaFormer is actually what you need" (vs "Attention is all you need").

DiffPool is a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Description and image from: Hierarchical Graph Representation Learning with Differentiable Pooling

DistDGL is a system for training GNNs in a mini-batch fashion on a cluster of machines. It is is based on the Deep Graph Library (DGL), a popular GNN development framework. DistDGL distributes the graph and its associated data (initial features and embeddings) across the machines and uses this distribution to derive a computational decomposition by following an owner-compute rule. DistDGL follows a synchronous training approach and allows ego-networks forming the mini-batches to include non-local nodes. To minimize the overheads associated with distributed computations, DistDGL uses a high-quality and light-weight mincut graph partitioning algorithm along with multiple balancing constraints. This allows it to reduce communication overheads and statically balance the computations. It further reduces the communication by replicating halo nodes and by using sparse embedding updates. The combination of these design choices allows DistDGL to train high-quality models while achieving high parallel efficiency and memory scalability

Wide&Deep jointly trains wide linear models and deep neural networks to combine the benefits of memorization and generalization for real-world recommender systems. In summary, the wide component is a generalized linear model. The deep component is a feed-forward neural network. The deep and wide components are combined using a weighted sum of their output log odds as the prediction. This is then fed to a logistic loss function for joint training, which is done by back-propagating the gradients from the output to both the wide and deep part of the model simultaneously using mini-batch stochastic optimization. The AdaGrad optimizer is used for the wider part. The combined model is illustrated in the figure (center).

A GNN for dags, which injects their topological order as an inductive bias via asynchronous message passing.

Graph Contrastive Coding is a self-supervised graph neural network pre-training framework to capture the universal network topological properties across multiple networks. GCC's pre-training task is designed as subgraph instance discrimination in and across networks and leverages contrastive learning to empower graph neural networks to learn the intrinsic and transferable structural representations.

ComiRec is a multi-interest framework for sequential recommendation. The multi-interest module captures multiple interests from user behavior sequences, which can be exploited for retrieving candidate items from the large-scale item pool. These items are then fed into an aggregation module to obtain the overall recommendation. The aggregation module leverages a controllable factor to balance the recommendation accuracy and diversity.

DCN-V2 is an architecture for learning-to-rank that improves upon the original DCN model. It first learns explicit feature interactions of the inputs (typically the embedding layer) through cross layers, and then combines with a deep network to learn complementary implicit interactions. The core of DCN-V2 is the cross layers, which inherit the simple structure of the cross network from DCN, however it is significantly more expressive at learning explicit and bounded-degree cross features.

DSelect-k is a continuously differentiable and sparse gate for Mixture-of-experts (MoE), based on a novel binary encoding formulation. Given a user-specified parameter $k$, the gate selects at most $k$ out of the $n$ experts. The gate can be trained using first-order methods, such as stochastic gradient descent, and offers explicit control over the number of experts to select. This explicit control over sparsity leads to a cardinality-constrained optimization problem, which is computationally challenging. To circumvent this challenge, the authors use a unconstrained reformulation that is equivalent to the original problem. The reformulated problem uses a binary encoding scheme to implicitly enforce the cardinality constraint. By carefully smoothing the binary encoding variables, the reformulated problem can be effectively optimized using first-order methods such as SGD. The motivation for this method is that existing sparse gates, such as Top-k, are not smooth. The lack of smoothness can lead to convergence and statistical performance issues when training with gradient-based methods.

MinCutPool is a trainable pooling operator for graphs that learns to map nodes into clusters. The method is trained to approximate the minimum K-cut of the graph to ensure that the clusters are balanced, while also jointly optimizing the objective of the task at hand.

\emph{Canonical partition} $\mathcal{P}$ crops the index-restricted d-hop neighborhood around the center node from the target graph. $\mathcal{D}(G_t,v_i,v_c)$ means the shortest distance between $v_i$ and $v_c$ on $G_t$. \begin{equation} \mathcal{P}(G_t, v_c, d) = G_c, \operatorname{ s.t. } G_c \subseteq G_t, V_c = { v_i \in V_t|\mathcal{D}(G_t,v_i,v_c) \leq d , v_i \leq v_c} \end{equation} The graph $G_c$ obtained by canonical partition is called the \emph{canonical neighborhood}. Canonical neighborhoods can correctly substitute the target graph in canonical count. The subgraph count of query in target equals the summation of the canonical count of query in canonical neighborhoods for all target nodes. Canonical neighborhoods are acquired with canonical partition $\mathcal{P}$, given any $d$ greater than the diameter of the query. \begin{equation} \mathcal{C}(G_q,G_t) = \sum_{v_c \in V_t} \mathcal{C}c(G_q, \mathcal{P}(G_t, v_c, d),v_c), d \geq \max{v_i, v_j \in V_q} \mathcal{D}(G_q, v_i, v_j) \end{equation}

Using cubic splines to improve factorization machine accuracy with numerical features

GAGNN, or Group-aware Graph Neural Network, is a hierarchical model for nationwide city air quality forecasting. The model constructs a city graph and a city group graph to model the spatial and latent dependencies between cities, respectively. GAGNN introduces differentiable grouping network to discover the latent dependencies among cities and generate city groups. Based on the generated city groups, a group correlation encoding module is introduced to learn the correlations between them, which can effectively capture the dependencies between city groups. After the graph construction, GAGNN implements message passing mechanism to model the dependencies between cities and city groups.

As they carry great potential for modeling complex interactions, graph neural network (GNN)-based methods have been widely used to predict quantum mechanical properties of molecules. Most of the existing methods treat molecules as molecular graphs in which atoms are modeled as nodes. They characterize each atom's chemical environment by modeling its pairwise interactions with other atoms in the molecule. Although these methods achieve a great success, limited amount of works explicitly take many-body interactions, i.e., interactions between three and more atoms, into consideration. In this paper, we introduce a novel graph representation of molecules, heterogeneous molecular graph (HMG) in which nodes and edges are of various types, to model many-body interactions. HMGs have the potential to carry complex geometric information. To leverage the rich information stored in HMGs for chemical prediction problems, we build heterogeneous molecular graph neural networks (HMGNN) on the basis of a neural message passing scheme. HMGNN incorporates global molecule representations and an attention mechanism into the prediction process. The predictions of HMGNN are invariant to translation and rotation of atom coordinates, and permutation of atom indices. Our model achieves state-of-the-art performance in 9 out of 12 tasks on the QM9 dataset.

The Multiplex Molecular Graph Neural Network (MXMNet) is an approach for the representation learning of molecules. The molecular interactions are divided into two categories: local and global. Then a two-layer multiplex graph $G = \\{ G_{l}, G_{g} \\}$ is constructed for a molecule. In $G$, the local layer $G_{l}$ only contains the local connections that mainly capture covalent interactions, and the global layer $G_{g}$ contains the global connections that cover non-covalent interactions. MXMNet uses the Multiplex Molecular (MXM) module that contains a novel angle-aware message passing operated on $G_{l}$ and an efficient message passing operated on $G_{g}$.

Point-GNN is a graph neural network for detecting objects from a LiDAR point cloud. It predicts the category and shape of the object that each vertex in the graph belongs to. In Point-GNN, there is an auto-registration mechanism to reduce translation variance, as well as a box merging and scoring operation to combine detections from multiple vertices accurately.

TaxoExpan is a self-supervised taxonomy expansion framework. It automatically generates a set of <query concept, anchor concept> pairs from the existing taxonomy as training data. Using such self-supervision data, TaxoExpan learns a model to predict whether a query concept is the direct hyponym of an anchor concept. TaxoExpan features: (1) a position-enhanced graph neural network that encodes the local structure of an anchor concept in the existing taxonomy, and (2) a noise-robust training objective that enables the learned model to be insensitive to the label noise in the self-supervision data.

Variational Quantum Singular Value Decomposition is a variational quantum algorithm for singular value decomposition (VQSVD). By exploiting the variational principles for singular values and the Ky Fan Theorem, a novel loss function is designed such that two quantum neural networks (or parameterized quantum circuits) could be trained to learn the singular vectors and output the corresponding singular values.