A team from **Facebook** **AI** **Research** say they’ve trained a **neural network** to solve advanced math at a moment’s thought. Before we delve into what it all means, let’s begin with a mathematical challenge.

In the differential equation below, solve for y. Quickly, you have only 30 seconds.

Do you have an answer?

It’s alright if you don’t know how to approach the math problem. The expression is so complex that even the most advanced mathematics software packages will struggle to find a solution – even after 30 seconds.

Meanwhile,** Guillaume Lample** and** FranÃ§ois Charton** at Facebook Research AI say they’ve developed an **algorithm** that can solve this problem in seconds. In other words, they successfully trained a neural network to perform the** symbolic reasoning** that’s required to differentiate and integrate mathematical expressions.

Here’s why it’s a big deal.

## Neural Network and Symbolic Reasoning

Among other things, neural networks are used for pattern-recognition tasks. These include object and face recognition, as well as certain kinds of **natural language processing**.

As accomplished as neural networks are today, training them to do symbolic reasoning tasks – which mathematics requires – has been challenging. At best, the algorithms would be able to perform addition and multiplication of whole numbers.

Like humans, neural networks find it challenging to decipher the **shorthands** which advanced mathematical expressions rely on.

For example, the expression *x ^{2}* is a shorthand form for x multiplied by x. Similarly, “multiplication” in this example is shorthand for repeated addition, which in turn is shorthand for the total value of two quantities combined.

Yes, it sounds a bit confusing.

But, the point is simple mathematical expressions are often a condensed expression of even simpler operations. And that’s why neural networks have struggled with this logic.

So, how did Facebook AI Research team overcome this issue?

## Training a Neural Network to Perform Advanced Math

First, the Facebook AI Research pair devised a smart way to unpack mathematical shorthands into its fundamental unit.

The researchers represented expressions as tree-like structures, with the leaves being constants, numbers, and variables like x. Then there are the internal nodes, which are operators like addition, subtraction, multiplication, differentiate-with-respect-to, etc.

Next, Lample and Charton had to train the neural network using an extensive database. They taught the model to recognize the patterns of manipulations that are equivalent to differentiation and integration.

In the end, the researchers tested the neural network on expressions it has never seen before. They entered 5,000 expressions into the system and compared the result it produced with commercially available solvers like **Matlab** and **Mathematica**.

The researchers noted:

“On all tasks, we observe that our model significantly outperforms Mathematica. On function integration, our model obtains close to 100% accuracy, while Mathematica barely reaches 85 percent.”

According to the team, Maple and Matlab packages didn’t perform any better.

While Facebook’s neural network may have outperformed the market leaders, the social media giant hasn’t announced plans to start a **symbolic** **algebra** service. With that said, the work shows a new way to apply neural networks beyond the traditional scope of pattern recognition.

By the way, the answer to the differential equation is:

Was that your answer?

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