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Graph Neural Networks (GNN) are a promising technique for bridging differential programming and combinatorial domains. … In summary, our work shows that Graph Neural Networks are powerful enough to solve mathcal{NP}-Complete problems which combine symbolic and numeric data.

## 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.

## Can machine learning solve NP problems?

So, to answer your question, no, machine learning algorithms cannot solve NP-complete or NP-hard problems.

## 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.

## Are NP-hard problems solvable?

(i) All NP-complete problems are solvable in polynomial time: Yes. Every problem in NP is polynomially reducible to SAT, and SAT is reducible to every NP-hard problem. … Since the set of NP-complete problems is a subset of NP, it follows that they are all solvable in polynomial time.

## Can neural networks model any function?

Summing up, a more precise statement of the universality theorem is that neural networks with a single hidden layer can be used to approximate any continuous function to any desired precision.

## Can neural networks 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!

## Is NLP NP-hard?

Yes, This problem is probably a tricky one, as you have mixed polynomials all over the place (x multiplied by y), hence many non-convexities. It is straightforward that when general Binary LPs are NP-hard then Binary NLPs are NP-hard too.

## 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 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.

## How hard is deep learning?

A third issue is that Deep Learning is a true Big Data technique that often relies on many millions of examples to come to a conclusion. … As one of the most difficult to learn tool sets with among the most limited fields of application, the other tools offer a far better return on the time invested.

## Why is my neural network so bad?

Your Network contains Bad Gradients. You Initialized your Network Weights Incorrectly. You Used a Network that was too Deep. You Used the Wrong Number of Hidden Units.

## How do you avoid local minima in neural networks?

However, weight adjusting with a gradient descent may result in the local minimum problem. Repeated training with random starting weights is among the popular methods to avoid this problem, but it requires extensive computational time.

## Are all NP problems NP-hard?

A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP. Conversely, a problem is NP-complete if it is both in NP and NP-hard. The NP-complete problems represent the hardest problems in NP.

## Can P be reduced to NP?

(If P and NP are the same class, then NP-intermediate problems do not exist because in this case every NP-complete problem would fall in P, and by definition, every problem in NP can be reduced to an NP-complete problem.)