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Posted by Eleni Triantafillou, Student Researcher, and Vincent Dumoulin, Research Scientist, Google Research

Recently, deep learning has achieved impressive performance on an array of challenging problems, but its success often relies on large amounts of manually annotated training data. This limitation has sparked interest in learning from fewer examples. A well-studied instance of this problem is few-shot image classification: learning new classes from only a few representative images.

In addition to being an interesting problem from a scientific perspective due to the apparent gap between the ability of a person to learn from limited information compared to that of a deep learning algorithm, few-shot classification is also a very important problem from a practical perspective. Because large labeled datasets are often unavailable for tasks of interest, solving this problem would enable, for example, quick customization of models to individual user’s needs, democratizing the use of machine learning. Indeed, there has been an explosion of recent work to tackle few-shot classification, but previous benchmarks fail to reliably assess the relative merits of the different proposed models, inhibiting research progress.

In “Meta-Dataset: A Dataset of Datasets for Learning to Learn from Few Examples” (presented at ICLR 2020), we propose a large-scale and diverse benchmark for measuring the competence of different image classification models in a realistic and challenging few-shot setting, offering a framework in which one can investigate several important aspects of few-shot classification. It is composed of 10 publicly available datasets of natural images (including ImageNet, CUB-200-2011, Fungi, etc.), handwritten characters and doodles. The code is public, and includes a notebook that demonstrates how Meta-Dataset can be used in TensorFlow and PyTorch. In this blog post, we outline some results from our initial research investigation on Meta-Dataset and highlight important research directions.

Background: Few-shot Classification
In standard image classification, a model is trained on a set of images from a particular set of classes, and then tested on a held-out set of images of those same classes. Few-shot classification goes a step further and studies generalization to entirely new classes at test time, no images of which were seen in training.

Specifically, in few-shot classification, the training set contains classes that are entirely disjoint from those that will appear at test time. So the aim of training is to learn a flexible model that can be easily repurposed towards classifying new classes using only a few examples. The end-goal is to perform well on the test-time evaluation that is carried out on a number of test tasks, each of which presents a classification problem between previously unseen classes, from a held out test set of classes. Each test task contains a support set of a few labeled images from which the model can learn about the new classes, and a disjoint query set of examples that the model is then asked to classify.

In Meta-Dataset, in addition to the tough generalization challenge to new classes inherent in the few-shot learning setup described above, we also study generalization to entirely new datasets, from which no images of any class were seen in training.

Comparison of Meta-Dataset with Previous Benchmarks
A popular dataset for studying few-shot classification is mini-ImageNet, a downsampled version of a subset of classes from ImageNet. This dataset contains 100 classes in total that are divided into training, validation and test class splits. While classes encountered at test time in benchmarks like mini-ImageNet have not been seen during training, they are still substantially similar to the training classes visually. Recent works reveal that this allows a model to perform competitively at test time simply by re-using features learned at training time, without necessarily demonstrating the capability to learn from the few examples presented to the model in the support set. In contrast, performing well on Meta-Dataset requires absorbing diverse information at training time and rapidly adapting it to solve significantly different tasks at test time that possibly originate from entirely unseen datasets.

Test tasks from mini-ImageNet. Each task is a classification problem between previously unseen (test) classes. The model can use the support set of a few labeled examples of the new classes to adapt to the task at hand and then predicts labels for the query examples of these new classes. The evaluation metric is the query set accuracy, averaged over examples within each task and across tasks.

While other recent papers have investigated training on mini-ImageNet and evaluating on different datasets, Meta-Dataset represents the largest-scale organized benchmark for cross-dataset, few-shot image classification to date. It also introduces a sampling algorithm for generating tasks of varying characteristics and difficulty, by varying the number of classes in each task, the number of available examples per class, introducing class imbalances and, for some datasets, varying the degree of similarity between the classes of each task. Some example test tasks from Meta-Dataset are shown below.

Test tasks from Meta-Dataset. Contrary to the mini-ImageNet tasks shown above, different tasks here originate from (the test classes of) different datasets. Further, the number of classes and the support set sizes differ across tasks and the support sets might be class-imbalanced.

Initial Investigation and Findings on Meta-Dataset
We benchmark two main families of few-shot learning models on Meta-Dataset: pre-training and meta-learning.

Pre-training simply trains a classifier (a neural network feature extractor followed by a linear classifier) on the training set of classes using supervised learning. Then, the examples of a test task can be classified either by fine-tuning the pre-trained feature extractor and training a new task-specific linear classifier, or by means of nearest-neighbor comparisons, where the prediction for each query example is the label of its nearest support example. Despite its “baseline” status in the few-shot classification literature, this approach has recently enjoyed a surge of attention and competitive results.

On the other hand, meta-learners construct a number of “training tasks” and their training objective explicitly reflects the goal of performing well on each task’s query set after having adapted to that task using the associated support set, capturing the ability that is required at test time to solve each test task. Each training task is created by randomly sampling a subset of training classes and some examples of those classes to play the role of support and query sets.

Below, we summarize some of our findings from evaluating pre-training and meta-learning models on Meta Dataset:

1) Existing approaches have trouble leveraging heterogeneous training data sources.

We compared training models (from both pre-training and meta-learning approaches) using only the training classes of ImageNet to using all training classes from the datasets in Meta-Dataset, in order to measure the generalization gain from using a more expansive collection of training data. We singled out ImageNet for this purpose, because the features learned on ImageNet readily transfer to other datasets. The evaluation tasks applied to all models are derived from a held-out set of classes from the datasets used in training, with at least two additional datasets that are entirely held-out for evaluation (i.e., no classes from these datasets were used for training).

One might expect that training on more data, albeit heterogeneous, would generalize better on the test set. However, this is not always the case. Specifically, the following figure displays the accuracy of different models on test tasks of Meta-Dataset’s ten datasets. We observe that the performance on test tasks coming from handwritten characters / doodles (Omniglot and Quickdraw) is significantly improved when having trained on all datasets, instead of ImageNet only. This is reasonable since these datasets are visually significantly different from ImageNet. However, for test tasks of natural image datasets, similar accuracy can be obtained by training on ImageNet only, revealing that current models cannot effectively leverage heterogeneous data towards improving in this regard.

Comparison of test performance on each dataset after having trained on ImageNet (ILSVRC-2012) only or on all datasets.

2) Some models are more capable than others of exploiting additional data at test time.

We analyzed the performance of different models as a function of the number of available examples in each test task, uncovering an interesting trade-off: different models perform best with a particular number of training (support) samples. We observe that some models outshine the rest when there are very few examples (“shots”) available (e.g., ProtoNet and our proposed fo-Proto-MAML) but don’t exhibit a large improvement when given more, while other models are not well-suited for tasks with very few examples but improve at a quicker rate as more are given (e.g., Finetune baseline). However, since in practice we might not know in advance the number of examples that will be available at test time, one would like to identify a model that can best leverage any number of examples, without disproportionately suffering in a particular regime.

Comparison of test performance averaged across different datasets to the number of examples available per class in test tasks (“shots”). Performance is measured in terms of class precision: the proportion of the examples of a class that are correctly labeled, averaged across classes.

3) The adaptation algorithm of a meta-learner is more heavily responsible for its performance than the fact that it is trained end-to-end (i.e. meta-trained).

We developed a new set of baselines to measure the benefit of meta-learning. Specifically, for several meta-learners, we consider a non-meta-learned counterpart that pre-trains a feature extractor and then, at evaluation time only, applies the same adaptation algorithm as the respective meta-learner on those features. When training on ImageNet only, meta-training often helps a bit or at least doesn’t hurt too much, but when training on all datasets, the results are mixed. This suggests that further work is needed to understand and improve upon meta-learning, especially across datasets.

Comparison of three different meta-learner variants to their corresponding inference-only baselines, when training on ImageNet (ILSVRC-1012) only or all datasets. Each bar represents the difference between meta-training and inference-only, so positive values indicate improved performance from meta-training.

Conclusion
Meta-Dataset introduces new challenges for few-shot classification. Our initial exploration has revealed limitations of existing methods, calling for additional research. Recent works have already reported exciting results on Meta-Dataset, for example using cleverly-designed task conditioning, more sophisticated hyperparameter tuning, a ‘meta-baseline’ that combines the benefits of pre-training and meta-learning, and finally using feature selection to specialize a universal representation for each task. We hope that Meta-Dataset will help drive research in this important sub-field of machine learning.

Acknowledgements
Meta-Dataset was developed by Eleni Triantafillou, Tyler Zhu, Vincent Dumoulin, Pascal Lamblin, Utku Evci, Kelvin Xu, Ross Goroshin, Carles Gelada, Kevin Swersky, Pierre-Antoine Manzagol and Hugo Larochelle. We would like to thank Pablo Castro for his valuable guidance on this blog post, Chelsea Finn for fruitful discussions and ensuring the correctness of fo-MAML’s implementation, as well as Zack Nado and Dan Moldovan for the initial dataset code that was adapted, Cristina Vasconcelos for spotting an issue in the ranking of models and John Bronskill for suggesting that we experiment with a larger inner-loop learning rate for MAML which indeed significantly improved our fo-MAML results.

Posted by Dami Choi, Student Researcher and George Dahl, Senior Research Scientist, Google Research

Over the past decade, dramatic increases in neural network training speed have made it possible to apply deep learning techniques to many important problems. In the twilight of Moore’s law, as improvements in general purpose processors plateau, the machine learning community has increasingly turned to specialized hardware to produce additional speedups. For example, GPUs and TPUs optimize for highly parallelizable matrix operations, which are core components of neural network training algorithms. These accelerators, at a high level, can speed up training in two ways. First, they can process more training examples in parallel, and second, they can process each training example faster. We know there are limits to the speedups from processing more training examples in parallel, but will building ever faster accelerators continue to speed up training?

Unfortunately, not all operations in the training pipeline run on accelerators, so one cannot simply rely on faster accelerators to continue driving training speedups. For example, earlier stages in the training pipeline like disk I/O and data preprocessing involve operations that do not benefit from GPUs and TPUs. As accelerator improvements outpace improvements in CPUs and disks, these earlier stages will increasingly become a bottleneck, wasting accelerator capacity and limiting training speed.

An example training pipeline representative of many large-scale computer vision programs. The stages that come before applying the mini-batch stochastic gradient descent (SGD) update generally do not benefit from specialized hardware accelerators.

Consider a scenario where the code upstream to the accelerator takes twice as long as the code that runs on the accelerator – a scenario that is already realistic for some workloads today. Even if the code is pipelined to execute the upstream and downstream stages in parallel, the upstream stage will dominate training time and the accelerator will be idle 50% of the time. In this case, building a faster accelerator will not improve training speed at all. It may be possible to speed up the input pipeline by dedicating engineering effort and additional compute resources, but such efforts are time consuming and distract from the main goal of improving predictive performance. For very small datasets,one can precompute the augmented dataset offline and load the entire preprocessed dataset in memory, but this doesn’t work for most ML training scenarios.

In “Faster Neural Network Training with Data Echoing”, we propose a simple technique that reuses (or “echoes”) intermediate outputs from earlier pipeline stages to reclaim idle accelerator capacity. Rather than waiting for more data to become available, we simply utilize data that is already available to keep the accelerators busy.

Left: Without data echoing, downstream computational capacity is idle 50% of the time. Right: Data echoing with echoing factor 2 reclaims downstream computational capacity.

Repeating Data to Train Faster
Imagine a situation where reading and preprocessing a batch of training data takes twice as long as performing a single optimization step on that batch. In this case, after the first optimization step on the preprocessed batch, we can reuse the batch and perform a second step before the next batch is ready. In the best case scenario, where repeated data is as useful as fresh data, we would see a twofold speedup in training. In reality, data echoing provides a slightly smaller speedup because repeated data is not as useful as fresh data – but it can still provide a significant speedup compared to leaving the accelerator idle.

There are typically several ways to implement data echoing in a given neural network training pipeline. The technique we propose involves duplicating data into a shuffle buffer somewhere in the training pipeline, but we are free to insert this buffer anywhere after whichever stage produces a bottleneck in the given pipeline. When we insert the buffer before batching, we call our technique example echoing, whereas, when we insert it after batching, we call our technique batch echoing. Example echoing shuffles data at the example level, while batch echoing shuffles the sequence of duplicate batches. We can also insert the buffer before data augmentation, such that each copy of repeated data is slightly different (and therefore closer to a fresh example). Of the different versions of data echoing that place the shuffle buffer between different stages, the version that provides the greatest speedup depends on the specific training pipeline.

Data Echoing Across Workloads
So how useful is reusing data? We tried data echoing on five neural network training pipelines spanning 3 different tasks – image classification, language modeling, and object detection – and measured the number of fresh examples needed to reach a particular performance target. We chose targets to match the best result reliably achieved by the baseline during hyperparameter tuning. We found that data echoing allowed us to reach the target performance with fewer fresh examples, demonstrating that reusing data is useful for reducing disk I/O across a variety of tasks. In some cases, repeated data is nearly as useful as fresh data: in the figure below, example echoing before augmentation reduces the number of fresh examples required almost by the repetition factor.

Data echoing, when each data item is repeated twice, either reduces or does not change the number of fresh examples needed to reach the target out-of-sample performance. Dashed lines indicate the values we would expect if repeated examples were as useful as fresh examples.

Reduction in Training Time
Data echoing can speed up training whenever computation upstream from accelerators dominates training time. We measured the training speedup achieved in a training pipeline bottlenecked by input latency due to streaming training data from cloud storage, which is realistic for many of today’s large-scale production workloads or anyone streaming training data over a network from a remote storage system. We trained a ResNet-50 model on the ImageNet dataset and found that data echoing provides a significant training speedup, in this case, more than 3 times faster when using data echoing.

Data echoing can reduce training time for ResNet-50 on ImageNet. In this experiment, reading a batch of training data from cloud storage took 6 times longer than the code that used each batch of data to perform a training step. The Echoing factor in the legend refers to the number of times each data item was repeated. Dashed lines indicate the expected values if repeated examples were as useful as fresh examples and there was no overhead from echoing.

Data Echoing Preserves Predictive Performance
Although one might be concerned that reusing data would harm the model’s final performance, we found that data echoing did not degrade the quality of the final model for any of the workloads we tested.

Comparing the individual trials that achieved the best out-of-sample performance during training for both with and without data echoing shows that reusing data does not harm final model quality. Here validation cross entropy is equivalent to log perplexity.

As improvements in specialized accelerators like GPUs and TPUs continue to outpace general purpose processors, we expect data echoing and similar strategies to become increasingly important parts of the neural network training toolkit.

Acknowledgements
The Data Echoing project was conducted by Dami Choi, Alexandre Passos, Christopher J. Shallue, and George E. Dahl while Dami Choi was a Google AI Resident. We would also like to thank Roy Frostig, Luke Metz, Yiding Jiang, and Ting Chen for helpful discussions.

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Posted by Yuxiang Yang and Deepali Jain, AI Residents, Robotics at Google

Recent advancements in deep reinforcement learning (deep RL) has enabled legged robots to learn many agile skills through automated environment interactions. In the past few years, researchers have greatly improved sample efficiency by using off-policy data, imitating animal behaviors, or performing meta learning. However, sample efficiency remains a bottleneck for most deep reinforcement learning algorithms, especially in the legged locomotion domain. Moreover, most existing works focus on simple, low-level skills only, such as walking forward, backward and turning. In order to operate autonomously in the real world, robots still need to combine these skills to generate more advanced behaviors.

Today we present two projects that aim to address the above problems and help close the perception-actuation loop for legged robots. In “Data Efficient Reinforcement Learning for Legged Robots”, we present an efficient way to learn low level motion control policies. By fitting a dynamics model to the robot and planning for actions in real time, the robot learns multiple locomotion skills using less than 5 minutes of data. Going beyond simple behaviors, we explore automatic path navigation in “Hierarchical Reinforcement Learning for Quadruped Locomotion”. With a policy architecture designed for end-to-end training, the robot learns to combine a high-level planning policy with a low-level motion controller, in order to navigate autonomously through a curved path.

Data Efficient Reinforcement Learning for Legged Robots
A major roadblock in RL is the lack of sample efficiency. Even with a state-of-the-art sample-efficient learning algorithm like Soft Actor-Critic (SAC), it would still require more than an hour of data to learn a reasonable walking policy, which is difficult to collect in the real world.

In a continued effort to learn walking skills using minimal interaction with the real-world environment, we present another, more sample-efficient model-based method for learning basic walking skills that dramatically reduces the training data needed. Instead of directly learning a policy that maps from environment state to robot action, we learn a dynamics model of the robot that estimates future states given its current state and action. Since the entire learning process requires less than 5 minutes of data, it could be performed directly on the real robot.

We start by executing random actions on the robot, and fit the model to the data collected. With the model fitted, we control the robot using a model predictive control (MPC) planner. We iterate between collecting more data with MPC and re-training the model to better fit the dynamics of the environment.

Overview of the model-based learning pipeline. The system alternates between fitting the dynamics model and collecting trajectories using model predictive control (MPC).

In standard MPC, the controller plans for a sequence of actions at each timestep, and only executes the first of the planned actions. While online replanning with regular feedback from the robot to the controller makes the controller robust to model inaccuracies, it also poses a challenge for the action planner, as planning must finish before the next step of the control loop (usually less than 10ms for legged robots). To satisfy such a tight time constraint, we introduce a multi-threaded, asynchronous version of MPC, with action planning and execution happening on different threads. As the execution thread applies actions at a high frequency, the planning thread optimizes for actions in the background without interruption. Furthermore, since action planning can take multiple timesteps, the robot state would have changed by the time planning has finished. To address the problem with planning latency, we devise a novel technique to compensate, which first predicts the future state when the planner is expected to finish its computation, and then uses this future state to seed the planning algorithm.

We separate action planning and execution on different threads.

Although MPC refreshes the action plan frequently, the planner still needs to work over long action horizons to keep track of the long-term goal and avoid myopic behaviors. To that end, we use a multi-step loss function, a reformulation of the model loss function that helps to reduce error accumulation over time by predicting the loss over a range of future steps.

Safety is another concern for learning on the real robot. For legged robots, a small mistake, such as missing a foot step, could lead to catastrophic failures, from the robot falling to the motor overheating. To ensure safe exploration, we embed a stable, in-place stepping gait prior, that is modulated by a trajectory generator. With the stable walking prior, MPC can then safely explore the action space.

Combining an accurate dynamics model with an online, asynchronous MPC controller, the robot successfully learned to walk using only 4.5 minutes of data (36 episodes). The learned dynamics model is also generalizable: by simply changing the reward function of MPC, the controller is able to optimize for different behaviors, such as walking backwards, or turning, without re-training. As an extension, we use a similar framework to enable even more agile behaviors. For example, in simulation the robot learns to backflip and walk on its rear legs, though these behaviors are yet to be learned by the real robot.

The robot learns to walk using only 4.5 minutes of data.

The robot learns to backflip and walk with rear legs using the same framework.

Combining low-level controller with high-level planning
Although model-based RL has allowed the robot to learn simple locomotion skills efficiently, such skills are insufficient for handling complex, real-world tasks. For example, in order to navigate through an office space, the robot may have to adjust its speed, direction and height multiple times, instead of following a pre-defined speed profile. Traditionally, people solve such complex tasks by breaking them down into multiple hierarchical sub-problems, such as a high-level trajectory planner and a low-level trajectory-following controller. However, manually defining a suitable hierarchy is typically a tedious task, as it requires careful engineering for each sub-problem.

In our second paper, we introduce a hierarchical reinforcement learning (HRL) framework that can be trained to automatically decompose complex reinforcement learning tasks. We break down our policy structure into a high-level and a low-level policy. Instead of designing each policy manually, we only define a simple communication protocol between the policy levels. In this framework, the high-level policy (e.g., a trajectory planner) commands the low-level policy (such as the motion control policy) through a latent command, and decides for how long to hold that command constant before issuing a new one. The low-level policy then interprets the latent command from the high-level policy, and gives motor commands to the robot.

To facilitate learning, we also split the observation space into high-level (e.g., robot position and orientation) and low-level (IMU, motor positions) observations, which are fed to their corresponding policies. This architecture naturally allows the high-level policy to operate at a slower timescale than the low-level policy, which saves computation resources and reduces training complexity.

Framework of Hierarchical Policy: The policy gets observations from the robot and sends motor commands to execute desired actions. It is split into two levels (high and low). The high-level policy gives a latent command to the low-level policy and also decides the duration for which low-level will run.

Since the high-level and low-level policies operate at discrete timescales, the entire policy structure is not end-to-end differentiable, and standard gradient-based RL algorithms like PPO and SAC cannot be used. Instead, we choose to train the hierarchical policy through augmented random search (ARS), a simple evolutionary optimization method that has demonstrated good performance in reinforcement learning tasks. Weights of both levels of the policy are trained together, where the objective is to maximize the total reward from the robot trajectory.

We test our framework on a path-following task using the same quadruped robot. In addition to straight walking, the robot needs to steer in different directions to complete the task. Note that as the low-level policy does not know the robot’s position in the path, it does not have sufficient information to complete the entire task on its own. However, with the coordination between the high-level and low-level policies, steering behavior emerges automatically in the latent command space, which allows the robot to efficiently complete the path. After successful training in a simulated environment, we validate our results on hardware by transferring an HRL policy to a real robot and recording the resulting trajectories.

Successful trajectory of a robot on a curved path. Left: A plot of the trajectory traversed by the robot with dots along the trajectory marking the positions where the high-level policy sent a new latent command to the low-level policy. Middle: The robot walking along the path in the simulated environment. Right: The robot walking around the path in the real world.

To further demonstrate the learned hierarchical policy, we visualized the behavior of the learned low-level policy under different latent commands. As shown in the plot below, different latent commands can cause the robot to walk straight, or turn left or right at different rates. We also test the generalizability of low-level policies by transferring them to new tasks from a similar domain, which, in our case, includes following a path with different shapes. By fixing the low-level policy weights and only training the high-level policy, the robot could successfully traverse through different paths.

Left: Visualization of a learned 2D latent command space. Vector directions correspond to the movement direction of the robot. Vector length is proportional to the distance covered. Right: Transfer of low level policy: An HRL policy was trained on a single path (right, top). The learned low-level policy was then reused when training the high-level policy on other paths (e.g., right, bottom).

Conclusion
Reinforcement learning poses a promising future for robotics by automating the controller design process. With model-based RL, we enabled efficient learning of generalizable locomotion behaviors directly on the real robot. With hierarchical RL, the robot learned to coordinate policies at different levels to achieve more complex tasks. In the future, we plan to bring perception into the loop, so that robots can operate truly autonomously in the real world.

Acknowledgements
Both Deepali Jain and Yuxiang Yang are residents in the AI Residency program, mentored by Ken Caluwaerts and Atil Iscen. We would also like to thank Jie Tan and Vikas Sindhwani for support of the research, and Noah Broestl for managing the New York AI Residency Program.

Posted by Anton Tsitsulin, Research Intern and Bryan Perozzi, Senior Research Scientist, Graph Mining Team, Google Research

Understanding the differences and similarities between complex datasets is an interesting challenge that often arises when working with data. One way to formalize this question is to view each dataset as a graph, a mathematical model for how items relate to each other. Graphs are widely used to model relationships between objects — the Internet graph connects pages referencing each other, social graphs link together friends, and molecule graphs connect atoms bonding with each other.

Graphs are discrete objects that can model the relationships between many different types of data, including web pages (left), social connections (center), or molecules (right).

Once there is a collection of multiple graphs, it is common to want to predict some property of each one as an aggregate (i.e., one label per graph). For example, consider the task of predicting protein function from structure: each dataset here is one protein, and the prediction task is whether the final structure encodes an enzyme or not. Since one wants a model to actually compute the prediction, we need a representation that lets us generalize across different protein structures. Ideally, one would want a way to represent graphs as vectors without costly labelling. The problem becomes harder with increasing graph size — in the molecule case humans possess some knowledge about their properties, however, reasoning about larger, more complex datasets becomes increasingly difficult.

In this post we highlight some recent advances in the area of graph representation learning with “Just SLaQ When You Approximate: Accurate Spectral Distances for Web-Scale Graphs” (published at WWW’20), a publication that improves on the scalability of our earlier research, “DDGK: Learning Graph Representations for Deep Divergence Graph Kernels” (published at WWW’19). SLaQ introduces a way to scale computations to approximate a certain class of graph statistics, allowing one to quickly and efficiently characterize large graphs. We are also happy to announce that we have released the code for both papers in the Google Research GitHub repository for graph embeddings.

Fully Unsupervised Learning of Graph Similarity
In our 2019 paper, we showed that it is possible to learn representations for graph similarity with neither domain knowledge nor supervision. We propose deep divergence graph kernels (DDGK), an unsupervised method for learning representations over graphs that encode mappings of similarities between them. Unlike previous work, our unsupervised method jointly learns node representations, graph representations, and an attention-based alignment between graphs.

Here is a t-SNE visualization of the latent representations learned by DDGK to compare proteins. Blue points indicate proteins that encode enzymes and the red points are for those that do not. We can see that the encoding correlates with a structural property of the protein (whether or not it encodes enzymes), even though this context was not provided during training. (Note that this is a projection of the representations, and so the absolute axis values aren’t meaningful.)

In the example above, we demonstrate how these representations can automatically learn to represent graphs and align them in a way that encodes their latent functional similarity. Experiments on other datasets show we can capture similarities and differences across graphs of different types (language, biology, and social interactions).

The pairwise distance between different datasets encoded and aligned using DDGK. Color indicates distance in the latent space, and the scale of similarity ranges from 0 (identical) to 1.0 (very different). We see that the representations can be clustered to group similar datasets together — for example, the datasets nci1 and ptc are both datasets of chemical compounds.

Fast and Accurate Approximation of Spectral Descriptors
A graph’s spectrum is a powerful representation that encodes its properties, including connectivity patterns between graph nodes and clustering information. The spectrum has been shown to convey rich information about the properties of different objects such as the sound of a drum, 3D shapes, graphs, and general high-dimensional data. Applications of spectral graph descriptors include AutoML systems, anomaly detection in dynamic graphs, and chemical molecule characterization.

Currently, learning-based systems such as DDGK do not scale to either large graphs or large graph collections. Alternatively, one can use the spectral information without the learning component to attain more desirable scaling properties. However, computing spectral descriptors for large graphs is computationally prohibitive. Our more recent paper addresses this problem by proposing SLaQ, a method for approximating a family of graph descriptors. Our approach uses a randomized approximation algorithm for computing traces of spectrum functions that allows us to study several well-known spectral graph characteristics like Von Neumann Graph Entropy, Estrada Index, graph energy, and NetLSD.

For example, we use SLaQ to monitor anomalous changes in the Wikipedia graph structure. SLaQ allows us to discern meaningful changes in the structure of the page graph from trivial ones such as mass page renames. Our experiments show two orders of magnitude improvement in approximation accuracy, on average.

Left: The well-known Karate graph represents the social interactions of two martial arts clubs. Right: The spectral descriptors (NetLSD, VNGE, and Estrada Index) computed for the original graph in blue and the version with removed edges in red.

Conclusions
Unsupervised representation learning for graphs is an important problem, and we believe that the methods we highlight here are exciting steps forward in this area! Specifically, SLaQ allows us to compute principled representations for vast datasets, and DDGK introduces a mechanism for automatically learning alignments between datasets. We hope that our contributions will help advance the analysis of large datasets, and will be useful for understanding changes to time-varying graph datasets, like those used in recommendation systems.

Acknowledgements
We thank Marina Munkhoeva, Rami Al-Rfou, and Dustin Zelle who contributed to these works. For more information on the Graph Mining team (part of Algorithm and Optimization Group) visit our pages.