Discrete Neural Algorithmic Reasoning

Neural algorithmic reasoning aims to capture computations with neural networks via learning the models to imitate the execution of classical algorithms. While common architectures are expressive enough to contain the correct model in the weights space, current neural reasoners are struggling to generalize well on out-of-distribution data. On the other hand, classical computations are not affected by distribution shifts as they can be described as transitions between discrete computational states. In this work, we propose to force neural reasoners to maintain the execution trajectory as a combination of finite predefined states. Trained with supervision on the algorithm's state transitions, such models are able to perfectly align with the original algorithm. To show this, we evaluate our approach on the SALSA-CLRS benchmark, where we get perfect test scores for all tasks. Moreover, the proposed architectural choice allows us to prove the correctness of the learned algorithms for any test data.

Neural Algorithmic Reasoning Without Intermediate Supervision

Neural Algorithmic Reasoning is an emerging area of machine learning focusing on building models which can imitate the execution of classic algorithms, such as sorting, shortest paths, etc. One of the main challenges is to learn algorithms that are able to generalize to out-of-distribution data, in particular with significantly larger input sizes. Recent work on this problem has demonstrated the advantages of learning algorithms step-by-step, giving models access to all intermediate steps of the original algorithm. In this work, we instead focus on learning neural algorithmic reasoning only from the input-output pairs without appealing to the intermediate supervision. We propose simple but effective architectural improvements and also build a self-supervised objective that can regularise intermediate computations of the model without access to the algorithm trajectory. We demonstrate that our approach is competitive to its trajectory-supervised counterpart on tasks from the CLRS Algorithmic Reasoning Benchmark and achieves new state-of-the-art results for several problems, including sorting, where we obtain significant improvements. Thus, learning without intermediate supervision is a promising direction for further research on neural reasoners.

Evaluating Robustness and Uncertainty of Graph Models Under Structural Distributional Shifts

In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be especially complex since the samples are interdependent. To evaluate the performance of graph models, it is important to test them on diverse and meaningful distributional shifts. However, most graph benchmarks that consider distributional shifts for node-level problems focus mainly on node features, while data in graph problems is primarily defined by its structural properties. In this work, we propose a general approach for inducing diverse distributional shifts based on graph structure. We use this approach to create data splits according to several structural node properties: popularity, locality, and density. In our experiments, we thoroughly evaluate the proposed distributional shifts and show that they are quite challenging for existing graph models. We hope that the proposed approach will be helpful for the further development of reliable graph machine learning.

A critical look at the evaluation of GNNs under heterophily: are we really making progress?

Node classification is a classical graph representation learning task on which Graph Neural Networks (GNNs) have recently achieved strong results. However, it is often believed that standard GNNs only work well for homophilous graphs, i.e., graphs where edges tend to connect nodes of the same class. Graphs without this property are called heterophilous, and it is typically assumed that specialized methods are required to achieve strong performance on such graphs. In this work, we challenge this assumption. First, we show that the standard datasets used for evaluating heterophily-specific models have serious drawbacks, making results obtained by using them unreliable. The most significant of these drawbacks is the presence of a large number of duplicate nodes in the datsets Squirrel and Chameleon, which leads to train-test data leakage. We show that removing duplicate nodes strongly affects GNN performance on these datasets. Then, we propose a set of heterophilous graphs of varying properties that we believe can serve as a better benchmark for evaluating the performance of GNNs under heterophily. We show that standard GNNs achieve strong results on these heterophilous graphs, almost always outperforming specialized models. Our datasets and the code for reproducing our experiments are available at https://github.com/yandex-research/heterophilous-graphs

Characterizing Graph Datasets for Node Classification: Beyond Homophily-Heterophily Dichotomy

Homophily is a graph property describing the tendency of edges to connect similar nodes; the opposite is called heterophily. While homophily is natural for many real-world networks, there are also networks without this property. It is often believed that standard message-passing graph neural networks (GNNs) do not perform well on non-homophilous graphs, and thus such datasets need special attention. While a lot of effort has been put into developing graph representation learning methods for heterophilous graphs, there is no universally agreed upon measure of homophily. Several metrics for measuring homophily have been used in the literature, however, we show that all of them have critical drawbacks preventing comparison of homophily levels between different datasets. We formalize desirable properties for a proper homophily measure and show how existing literature on the properties of classification performance metrics can be linked to our problem. In doing so we find a measure that we call adjusted homophily that satisfies more desirable properties than existing homophily measures. Interestingly, this measure is related to two classification performance metrics - Cohen's Kappa and Matthews correlation coefficient. Then, we go beyond the homophily-heterophily dichotomy and propose a new property that we call label informativeness (LI) that characterizes how much information a neighbor's label provides about a node's label. We theoretically show that LI is comparable across datasets with different numbers of classes and class size balance. Through a series of experiments we show that LI is a better predictor of the performance of GNNs on a dataset than homophily. We show that LI explains why GNNs can sometimes perform well on heterophilous datasets - a phenomenon recently observed in the literature.

Gradient Boosting Performs Low-Rank Gaussian Process Inference

This paper shows that gradient boosting based on symmetric decision trees can be equivalently reformulated as a kernel method that converges to the solution of a certain Kernel Ridgeless Regression problem. Thus, for low-rank kernels, we obtain the convergence to a Gaussian Process' posterior mean, which, in turn, allows us to easily transform gradient boosting into a sampler from the posterior to provide better knowledge uncertainty estimates through Monte-Carlo estimation of the posterior variance. We show that the proposed sampler allows for better knowledge uncertainty estimates leading to improved out-of-domain detection.

Which Tricks are Important for Learning to Rank?

Nowadays, state-of-the-art learning-to-rank (LTR) methods are based on gradient-boosted decision trees (GBDT). The most well-known algorithm is LambdaMART that was proposed more than a decade ago. Recently, several other GBDT-based ranking algorithms were proposed. In this paper, we conduct a thorough analysis of these methods in a unified setup. In particular, we address the following questions. Is direct optimization of a smoothed ranking loss preferable over optimizing a convex surrogate? How to properly construct and smooth surrogate ranking losses? To address these questions, we compare LambdaMART with YetiRank and StochasticRank methods and their modifications. We also improve the YetiRank approach to allow for optimizing specific ranking loss functions. As a result, we gain insights into learning-to-rank approaches and obtain a new state-of-the-art algorithm.

Good Classification Measures and How to Find Them

Several performance measures can be used for evaluating classification results: accuracy, F-measure, and many others. Can we say that some of them are better than others, or, ideally, choose one measure that is best in all situations? To answer this question, we conduct a systematic analysis of classification performance measures: we formally define a list of desirable properties and theoretically analyze which measures satisfy which properties. We also prove an impossibility theorem: some desirable properties cannot be simultaneously satisfied. Finally, we propose a new family of measures satisfying all desirable properties except one. This family includes the Matthews Correlation Coefficient and a so-called Symmetric Balanced Accuracy that was not previously used in classification literature. We believe that our systematic approach gives an important tool to practitioners for adequately evaluating classification results.

Shifts: A Dataset of Real Distributional Shift Across Multiple Large-Scale Tasks

There has been significant research done on developing methods for improving robustness to distributional shift and uncertainty estimation. In contrast, only limited work has examined developing standard datasets and benchmarks for assessing these approaches. Additionally, most work on uncertainty estimation and robustness has developed new techniques based on small-scale regression or image classification tasks. However, many tasks of practical interest have different modalities, such as tabular data, audio, text, or sensor data, which offer significant challenges involving regression and discrete or continuous structured prediction. Thus, given the current state of the field, a standardized large-scale dataset of tasks across a range of modalities affected by distributional shifts is necessary. This will enable researchers to meaningfully evaluate the plethora of recently developed uncertainty quantification methods, as well as assessment criteria and state-of-the-art baselines. In this work, we propose the \emph{Shifts Dataset} for evaluation of uncertainty estimates and robustness to distributional shift. The dataset, which has been collected from industrial sources and services, is composed of three tasks, with each corresponding to a particular data modality: tabular weather prediction, machine translation, and self-driving car (SDC) vehicle motion prediction. All of these data modalities and tasks are affected by real, `in-the-wild' distributional shifts and pose interesting challenges with respect to uncertainty estimation. In this work we provide a description of the dataset and baseline results for all tasks.