Tag Archives: general interest

Issues with graph neural networks: the cracks are where the light shines through

Deep convolutional neural networks have lead to astonishing breakthroughs in the area of computer vision in recent years. The reason for the extraordinary performance of convolutional architectures in the image domain is their strong ability to extract informative high-level features from visual data. For prediction tasks on images, this has lead to superhuman performance in a variety of applications and to an almost universal shift from classical feature engineering to differentiable feature learning.

Unfortunately, the picture is not quite as rosy yet in the area of molecular machine learning. Feature learning techniques which operate directly on raw molecular graphs without intermediate feature-engineering steps have only emerged in the last few years in the form of graph neural networks (GNNs). GNNs, however, still have not managed to definitively outcompete and replace more classical non-differentiable molecular representation methods such as extended-connectivity fingerprints (ECFPs). There is an increasing awareness in the computational chemistry community that GNNs have not quite lived up to the initial hype and still suffer from a number of technical limitations.

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Chained or Unchained: Markov, Nekrasov and Free Will

A Markov Chain moving between two states A and B. Animation by Devin Soni

Markov chains are simple probabilistic models which model sequences of related events through time. In a Markov chain, events at the present time depend on the previous event in the sequence. The example above shows a model of a dynamical system with two states A and B and the events are either moving between states A and B, or staying put.

More formally, a Markov chain is a model of any sequence of events with the following relationship

P(X_t=x|X_{t-1}=x_{t-1},X_{t-2}=x_{t-2},..,X_1=x_1)=P(X_t|X_{t-1}).

That is, the event that the sequence \{X_t\}_{t} is in state x at time t is conditionally independent of all of its past states given its immediate past. This simple relationship between past and present provides a useful simplifying assumption to model, to a surprising degree of accuracy, many real world systems. These range from air particles diffusing through a room, to the migration patterns of insects, to the evolution of your genome, and even your web browser activity. Given their broad use in describing natural phenomena, it is very curious that Markov first invented the Markov chain to settle a dispute in Mathematical Theology, one in which the atheist Markov was pitted against the devoutly Orthodox Pavel Nekrasov.

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