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Which problems in AI are not machine learning? Which problems involve both AI and machine learning?

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Before it's possible to define Artificial Intelligence outside of machine learning, i want to introduce first the limitations of neural networks with an example. In nearly all practical discussions about machine learning a common question is seen very often: A newbie has trained his 10 layer tensorflow network, has utilized a recent learning algorithm and is trying to play a game autonomously. At first, the neural network is able to reduce the error rate, that means, the controller on the screen gets improved, but after a while the error rate remains constant and didn't come down to zero. That means, the neural network isn't able to play the game and even a faster graphics card doesn't change the situation. Stopping the learning progress can be called a limitation in Deeplearning.

Now we can try to answer what Artificial Intelligence outside of machine learning has to offer which will overcome this bottleneck. At foremost, Artificial Intelligence outside of machine learning has developed some techniques which are helping to reduce the state space with symbolic manipulation. Some examples are: ontologies, macro-operators and frames (Marvin Minsky). None of these problem solving techniques is using Deeplearning directly. Instead they are providing concepts which are located in classical computer science, for example compilerdesign, Chomsky grammars and Planning. If these classical symbolic AI techniques are used to provide a model and this model gets trained by a neural network it's possible to overcome the bottleneck in machine learning and reduce the error rate down to zero.

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This is a common question and it has already been answered in many different places:

What is the difference between artificial intelligence and machine learning?

Artificial Intelligence vs. Machine Learning vs. Deep Learning

Artificial intelligence is a broader concept than machine learning, which addresses the use of computers to mimic the cognitive functions of humans. When machines carry out tasks based on algorithms in an "intelligent" manner, that is AI. Machine learning is a subset of AI and focuses on the ability of machines to receive a set of data and learn for themselves, changing algorithms as they learn more about the information they are processing.

More specific to your question:

AI without machine learning

If you insert a small amount of knowledge into a machine, you can call it an engineering product. But if you instill a sufficiently large amount of knowledge such that the machine makes better decisions than a human, that can be could AI. For example, if you take hundreds of medical doctors and each spends hundreds of hours detailing correlations between symptoms and disease, if you then pack that knowledge into an easy-to-use machine, that's AI without machine-learning

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