When the bridge was built, we simply did not have a good enough theory about the aerodynamical forces that a bridge is e

This was written in the immediate aftermath of my husband’s death by suicide. My knowledge of mental illness has evolved, with the help of much therapy for all four of us, since then. I’m sharing our experience in the hopes that it may help one family out there struggling.

Modern machine learning research has demonstrated remarkable achievements. Today, we can train machines to detect objects in images, extract meaning from text, stop spam emails, drive cars, discover new drug candidates, and beat top players in Chess, Go, and countless other games.

Perhaps the most important concept in physics is that of emergence: higher-level theories describing macro-phenomena mathematically emerge from lower-level theories describing micro-phenomena. When talking about a gas, for example, it quickly becomes unfeasible to talk about the properties of the individual particles making up that gas. Instead, it is more meaningful and useful to treat macroscopic quantities like pressure, temperature, and entropy as the fundamental properties. The equations of statistical mechanics then describe how these macro-quantities relate to the states of the underlying particles.

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ero observed activity in two Facebook groups named for the Stop the Steal movement, a Republican-funded disinformation campaign falsely claiming the presidential election was stolen from President Trump. Together, the groups counted nearly 100,000 people among their members and behaved as an echo chamber for conspiracy theories, such as the thoroughly debunked allegation that Dominion voting machines were manipulated to change votes for Trump to votes for Joe Biden. One of the groups, which had more than 12,000 members, was private so as to avoid moderation. At the time of OneZero’s reporting, the other group, which remained public, was debating whether or not to go private.

We have some guidance from mathematics. In a 1989 paper, mathematician George Cybenko, then a researcher at the University of Illinois in Urbana, proofed the Universal Approximation Theorem: for any continuous function f, there exists a single-layer neural network that can approximate f arbitrarily well, as long as the activation function of that network is sigmoid-like.

Lacking a complete theory, we have to rely on intuition. Deeper neural network architectures, so the common intuition, generalize better and overfit less. They achieve this by learning hierarchies of representations: in face detection, for instance, these could be edges and lines at the bottom, eyes near the top, and complete faces at the top of the hierarchy. Even if part of the face is hidden, the network will still pick up a signal from the remaining input, and therefore generalize better.

A lot of these advancements are powered by deep learning, in particular deep neural networks. Yet, the theory behind deep neural networks remains poorly understood. Sure, we understand the math of what individual neurons are doing, but we’re lacking a mathematical theory of the emergent behavior of entire network. What makes deep neural networks so powerful?

It’s a good intuition, and it appears to be what is actually happening. Experiments confirm that deep neural networks outperform shallow ones on common image as well as text tasks. But it’s just that, an intuition. We don’t have a complete mathematical theory explaining why this intuition should be true.

Compare this situation to physics. Physics, more than any other discipline, has embraced the symbiosis of experiment and theory. The ‘standard model’ of particle physics, for instance, describes the properties of the fundamental particles that make up our universe, and how these particles are allowed to interact. The theory then guides the design of new experiments. For example, the discovery of the Higgs particle back in 2012 at CERN was possible because theory told us where to look. Theory, in other words, guides our intuition.

This is quite a remarkable result, but there’s a catch: in practice, we not only want a neural network that approximates well on data we have seen. We also want it to work well on unseen data. The theorem, in other words, is silent about the problem of overfitting.

If you are experiencing thoughts of self-harm or suicide, please do not hesitate to contact the National Suicide Prevention Lifeline at 1-800-273-TALK (8255). This is a free, 24/7 confidential service that can provide people in suicidal crisis or emotional distress, or those around them, with support, information, and local resources. For more information, call or visit SuicidePreventionLifeline.org.

If you are experiencing thoughts of self-harm or suicide, please do not hesitate to contact the National Suicide Prevention Lifeline at 1-800-273-TALK (8255). This is a free, 24/7 confidential service that can provide people in suicidal crisis or emotional distress, or those around them, with support, information, and local resources. For more information, call or visit SuicidePreventionLifeline.org.

The story of the Tacoma Narrows bridge illustrates vividly why it is so important to have a good theory. After being opened for traffic in July 1940, the bridge started swaying wildly in the wind, until it spectacularly collapsed just 4 months later. One dog died.

Every step I took up our driveway made my legs quake, knowing, as I got closer to our front door, that I was about to cross a line separating “before” and “after,” and nothing would ever be the same.

Theory also provides a safeguard against fluke discoveries. When researchers from the OPERA experiment announced in 2011 that they had measured neutrinos that were moving faster than the speed of light, we knew from our theories that this was an extraordinary statement, and needed to be vetted carefully. Indeed, as it was discovered later, a fiber optic cable had been attached improperly, causing the erroneous readings.