Training Graph Neural Networks (GNNs) on large graphs presents unique challenges due to the large memory and computing requirements. Distributed GNN training, where the graph is partitioned across multiple machines, is a common approach to training GNNs on large graphs. However, as the graph cannot generally be decomposed into small non-interacting components, data communication between the training machines quickly limits training speeds. Compressing the communicated node activations by a fixed amount improves the training speeds, but lowers the accuracy of the trained GNN. In this paper, we introduce a variable compression scheme for reducing the communication volume in distributed GNN training without compromising the accuracy of the learned model. Based on our theoretical analysis, we derive a variable compression method that converges to a solution equivalent to the full communication case, for all graph partitioning schemes. Our empirical results show that our method attains a comparable performance to the one obtained with full communication. We outperform full communication at any fixed compression ratio for any communication budget.

Foundation models that can perform inference on any new task without requiring specific training have revolutionized machine learning in vision and language applications. However, applications involving graph-structured data remain a tough nut for foundation models, due to challenges in the unique feature- and label spaces associated with each graph. Traditional graph ML models such as graph neural networks (GNNs) trained on graphs cannot perform inference on a new graph with feature and label spaces different from the training ones. Furthermore, existing models learn functions specific to the training graph and cannot generalize to new graphs. In this work, we tackle these two challenges with a new foundational architecture for inductive node classification named GraphAny. GraphAny models inference on a new graph as an analytical solution to a LinearGNN, thereby solving the first challenge. To solve the second challenge, we learn attention scores for each node to fuse the predictions of multiple LinearGNNs. Specifically, the attention module is carefully parameterized as a function of the entropy-normalized distance-features between multiple LinearGNNs predictions to ensure generalization to new graphs. Empirically, GraphAny trained on the Wisconsin dataset with only 120 labeled nodes can effectively generalize to 30 new graphs with an average accuracy of 67.26\% in an inductive manner, surpassing GCN and GAT trained in the supervised regime, as well as other inductive baselines.

Foundation models in language and vision have the ability to run inference on any textual and visual inputs thanks to the transferable representations such as a vocabulary of tokens in language. Knowledge graphs (KGs) have different entity and relation vocabularies that generally do not overlap. The key challenge of designing foundation models on KGs is to learn such transferable representations that enable inference on any graph with arbitrary entity and relation vocabularies. In this work, we make a step towards such foundation models and present ULTRA, an approach for learning universal and transferable graph representations. ULTRA builds relational representations as a function conditioned on their interactions. Such a conditioning strategy allows a pre-trained ULTRA model to inductively generalize to any unseen KG with any relation vocabulary and to be fine-tuned on any graph. Conducting link prediction experiments on 57 different KGs, we find that the zero-shot inductive inference performance of a single pre-trained ULTRA model on unseen graphs of various sizes is often on par or better than strong baselines trained on specific graphs. Fine-tuning further boosts the performance.

We present the Sequential Aggregation and Rematerialization (SAR) scheme for distributed full-batch training of Graph Neural Networks (GNNs) on large graphs. Large-scale training of GNNs has recently been dominated by sampling-based methods and methods based on non-learnable message passing. SAR on the other hand is a distributed technique that can train any GNN type directly on an entire large graph. The key innovation in SAR is the distributed sequential rematerialization scheme which sequentially re-constructs then frees pieces of the prohibitively large GNN computational graph during the backward pass. This results in excellent memory scaling behavior where the memory consumption per worker goes down linearly with the number of workers, even for densely connected graphs. Using SAR, we report the largest applications of full-batch GNN training to-date, and demonstrate large memory savings as the number of workers increases. We also present a general technique based on kernel fusion and attention-matrix rematerialization to optimize both the runtime and memory efficiency of attention-based models. We show that, coupled with SAR, our optimized attention kernels lead to significant speedups and memory savings in attention-based GNNs.

Recent improvements in the performance of state-of-the-art (SOTA) methods for Graph Representational Learning (GRL) have come at the cost of significant computational resource requirements for training, e.g., for calculating gradients via backprop over many data epochs. Meanwhile, Singular Value Decomposition (SVD) can find closed-form solutions to convex problems, using merely a handful of epochs. In this paper, we make GRL more computationally tractable for those with modest hardware. We design a framework that computes SVD of \textit{implicitly} defined matrices, and apply this framework to several GRL tasks. For each task, we derive linear approximation of a SOTA model, where we design (expensive-to-store) matrix $\mathbf{M}$ and train the model, in closed-form, via SVD of $\mathbf{M}$, without calculating entries of $\mathbf{M}$. By converging to a unique point in one step, and without calculating gradients, our models show competitive empirical test performance over various graphs such as article citation and biological interaction networks. More importantly, SVD can initialize a deeper model, that is architected to be non-linear almost everywhere, though behaves linearly when its parameters reside on a hyperplane, onto which SVD initializes. The deeper model can then be fine-tuned within only a few epochs. Overall, our procedure trains hundreds of times faster than state-of-the-art methods, while competing on empirical test performance. We open-source our implementation at: https://github.com/samihaija/isvd

Many recent works have studied the performance of Graph Neural Networks (GNNs) in the context of graph homophily - a label-dependent measure of connectivity. Traditional GNNs generate node embeddings by aggregating information from a node's neighbors in the graph. Recent results in node classification tasks show that this local aggregation approach performs poorly in graphs with low homophily (heterophilic graphs). Several mechanisms have been proposed to improve the accuracy of GNNs on such graphs by increasing the aggregation range of a GNN layer, either through multi-hop aggregation, or through long-range aggregation from distant nodes. In this paper, we show that properly tuned classical GNNs and multi-layer perceptrons match or exceed the accuracy of recent long-range aggregation methods on heterophilic graphs. Thus, our results highlight the need for alternative datasets to benchmark long-range GNN aggregation mechanisms. We also show that homophily is a poor measure of the information in a node's local neighborhood and propose the Neighborhood Information Content (NIC) metric, which is a novel information-theoretic graph metric. We argue that NIC is more relevant for local aggregation methods as used by GNNs. We show that, empirically, it correlates better with GNN accuracy in node classification tasks than homophily.

We present a recurrent neuronal network, modeled as a continuous-time dynamical system, that can solve constraint satisfaction problems. Discrete variables are represented by coupled Winner-Take-All (WTA) networks, and their values are encoded in localized patterns of oscillations that are learned by the recurrent weights in these networks. Constraints over the variables are encoded in the network connectivity. Although there are no sources of noise, the network can escape from local optima in its search for solutions that satisfy all constraints by modifying the effective network connectivity through oscillations. If there is no solution that satisfies all constraints, the network state changes in a pseudo-random manner and its trajectory approximates a sampling procedure that selects a variable assignment with a probability that increases with the fraction of constraints satisfied by this assignment.

Batch-normalization (BN) layers are thought to be an integrally important layer type in today's state-of-the-art deep convolutional neural networks for computer vision tasks such as classification and detection. However, BN layers introduce complexity and computational overheads that are highly undesirable for training and/or inference on low-power custom hardware implementations of real-time embedded vision systems such as UAVs, robots and Internet of Things (IoT) devices. They are also problematic when batch sizes need to be very small during training, and innovations such as residual connections introduced more recently than BN layers could potentially have lessened their impact. In this paper we aim to quantify the benefits BN layers offer in image classification networks, in comparison with alternative choices. In particular, we study networks that use shifted-ReLU layers instead of BN layers. We found, following experiments with wide residual networks applied to the ImageNet, CIFAR 10 and CIFAR 100 image classification datasets, that BN layers do not consistently offer a significant advantage. We found that the accuracy margin offered by BN layers depends on the data set, the network size, and the bit-depth of weights. We conclude that in situations where BN layers are undesirable due to speed, memory or complexity costs, that using shifted-ReLU layers instead should be considered; we found they can offer advantages in all these areas, and often do not impose a significant accuracy cost.

Deep neural networks are typically highly over-parameterized with pruning techniques able to remove a significant fraction of network parameters with little loss in accuracy. Recently, techniques based on dynamic re-allocation of non-zero parameters have emerged for training sparse networks directly without having to train a large dense model beforehand. We present a parameter re-allocation scheme that addresses the limitations of previous methods such as their high computational cost and the fixed number of parameters they allocate to each layer. We investigate the performance of these dynamic re-allocation methods in deep convolutional networks and show that our method outperforms previous static and dynamic parameterization methods, yielding the best accuracy for a given number of training parameters, and performing on par with networks obtained by iteratively pruning a trained dense model. We further investigated the mechanisms underlying the superior performance of the resulting sparse networks. We found that neither the structure, nor the initialization of the sparse networks discovered by our parameter reallocation scheme are sufficient to explain their superior generalization performance. Rather, it is the continuous exploration of different sparse network structures during training that is critical to effective learning. We show that it is more fruitful to explore these structural degrees of freedom than to add extra parameters to the network.

Error backpropagation is a highly effective mechanism for learning high-quality hierarchical features in deep networks. Updating the features or weights in one layer, however, requires waiting for the propagation of error signals from higher layers. Learning using delayed and non-local errors makes it hard to reconcile backpropagation with the learning mechanisms observed in biological neural networks as it requires the neurons to maintain a memory of the input long enough until the higher-layer errors arrive. In this paper, we propose an alternative learning mechanism where errors are generated locally in each layer using fixed, random auxiliary classifiers. Lower layers could thus be trained independently of higher layers and training could either proceed layer by layer, or simultaneously in all layers using local error information. We address biological plausibility concerns such as weight symmetry requirements and show that the proposed learning mechanism based on fixed, broad, and random tuning of each neuron to the classification categories outperforms the biologically-motivated feedback alignment learning technique on the MNIST, CIFAR10, and SVHN datasets, approaching the performance of standard backpropagation. Our approach highlights a potential biological mechanism for the supervised, or task-dependent, learning of feature hierarchies. In addition, we show that it is well suited for learning deep networks in custom hardware where it can drastically reduce memory traffic and data communication overheads.