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In summary, our work shows that Graph Neural Networks are powerful enough to solve mathcal{NP}-Complete problems which combine symbolic and numeric data.

## Are neural networks NP-hard?

Training deep learning neural networks is very challenging. The best general algorithm known for solving this problem is stochastic gradient descent, where model weights are updated each iteration using the backpropagation of error algorithm. Optimization in general is an extremely difficult task.

## Can you solve NP-hard problems?

NP-Hard problems(say X) can be solved if and only if there is a NP-Complete problem(say Y) that can be reducible into X in polynomial time. NP-Complete problems can be solved by a non-deterministic Algorithm/Turing Machine in polynomial time.

## Can neural networks solve any problem?

A feedforward network with a single layer is sufficient to represent any function, but the layer may be infeasibly large and may fail to learn and generalize correctly. … If you accept most classes of problems can be reduced to functions, this statement implies a neural network can, in theory, solve any problem.

## Are neural networks NP-complete?

Theorem: Training a 3-node neural network is NP-complete. one hidden node are required to equal the corresponding weights of the other, so possibly only the thresholds differ, and even if any or all of the weights are forced to be from {+ 1, -I}.

## Can machine learning solve NP-hard?

Machine learning probably can’t be used to solve NP-complete problems in polynomial time.

## Why are deep neural networks hard to train?

More generally, it turns out that the gradient in deep neural networks is unstable, tending to either explode or vanish in earlier layers. This instability is a fundamental problem for gradient-based learning in deep neural networks. It’s something we need to understand, and, if possible, take steps to address.

## How do you show NP-hard?

By definition P is contained in NP. If P NP, then any problem that is in P (also in NP) can’t be NP-hard. So the whole class P will be a positive candidate for this question. If P=NP, then all NP problems will be NP-hard under polynomial time reductions.

## Can all NP-hard problems be solved in exponential time?

Yes, every NP problem has an exponential-time algorithm.

## Is chess NP-hard?

As a decision problem, it’s complexity is characterized as EXPTIME-complete as the proof also requires an exponential time to check. Due to the same reason, it cannot be in NP. Chess comes under NP Hard problem.

## Can neural network learn any function?

In summary, neural networks are powerful machine learning tools because of their ability to (in theory) learn any function. This is not a guarantee, however, that you will easily find the optimal weights for a given problem!

## Can neural network learn anything?

‘ Having said that, yes, a neural network can ‘learn’ from experience. In fact, the most common application of neural networks is to ‘train’ a neural network to produce a specific pattern as its output when it is presented with a given pattern as its input.

## What are the problems of neural network?

3. Amount of Data. Neural networks usually require much more data than traditional machine learning algorithms, as in at least thousands if not millions of labeled samples. This isn’t an easy problem to deal with and many machine learning problems can be solved well with less data if you use other algorithms.

## Is reinforcement learning NP-hard?

Conclusion. Most real-world reinforcement learning problems have incredibly complicated state and/or action spaces. Despite the fact that the fully-observable MDP is P-complete, most realistic MDPs are partially-observed, which we have established as being an NP-hard problem at best.

## Can NP-complete problems be solved in polynomial time?

If an NP-complete problem can be solved in polynomial time then all problems in NP can be solved in polynomial time. If a problem in NP cannot be solved in polynomial time then all problems in NP-complete cannot be solved in polynomial time. Note that an NP-complete problem is one of those hardest problems in NP.

## Is deep learning NP-complete?

When you look at what deep learning actually does, it is obvious that deep learning is nowhere near solving NP-complete problems in polynomial time or solving them at all.