# Questions tagged [math]

For questions about mathematics related to artificial intelligence.

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### Where does the expectation term in the derivative of the soft-max policy come from?

At slide 17 of the David Silver's series, the soft-max policy is defined as follows $$\pi_\theta(s, a) \propto e^{\phi(s, a)^T \theta}$$ that is, the probability of an action $a$ (in state $s$) is ...
3k views

### Why do activation functions need to be differentiable in the context of neural networks?

Why should an activation function of a neural network be differentiable? Is it strictly necessary or is it just advantageous?
160 views

### How are vectors and matrices multiplied in supervised machine learning?

I've recently started reading a book about deep learning. The book is titled "Grokking Deep Learning" (by Andrew W Trask). In chapter 3 (pages 44 and 45), it talks about multiplying vectors using dot ...
18k views

### Is it possible to train the neural network to solve math equations?

I'm aware that neural networks are probably not designed to do that, however asking hypothetically, is it possible to train the deep neural network (or similar) to solve math equations? So given the ...
241 views

I have followed the pseudocode in the ADADELTA paper (top right on page 3), and wrote the following Python code for solving the optimization problem L(x) = x^2: ...
26 views

### Since there are different types of neurons in adjacent positions in the brain's arrays, should heterogeneous layers be developed?

Below is a taxonomy of neurons. Some of these types occur in different locations in the brain, but there are adjacent neurons of varying types with clearly functional type diversity in many parts of ...
669 views

### Is known math really enough for AI

As an Electronics & Communication Engineering student I've heard some stories and theories about "The math we have is not enough to complete a thinker-learner AI." What is the truth? Is humankind ...
509 views

### Is recursion used in practice to improve performance of AI systems?

Is there any methods by which artificial intelligence use recursion(s) to solve a certain issue or to keep up working and calculating?
804 views

### Are FFNN (MLP) Lipschitz functions?

My question is regarding standard dense-connected feed forward neural networks with sigmoidal activation. I am studying Bayesian Optimization for hyper-parameter selection for neural networks. There ...
43 views

### When will we have computer programs that can compose mathematical proofs?

When will it be possible to give a computer program a bunch of assumptions and ask it if a certain statement is true or false, giving a proof or a counterexample respectively?
296 views

### Solving equations using reinforcement learning

I was lately curious about a reinforcement learning approach that would solve maths equations. For example, if I have the following equation:  f(g(h(w))) = 0 , with \ w = \begin{matrix} a_{11} &...
87 views

### Reward-related formulation in reinforcement learning

I am referring to eq. 3.6 (p/g 49) based on Sutton's online book and can be found in an image below. I could not make sense of the final derivation of the equation $r(s, a, s')$. My question is ...
517 views

### Why is the derivative 0 if the policy is deterministic?

In the Berkeley RL class they mention the gradient would be 0 if the policy is deterministic. Why is that? https://www.youtube.com/watch?v=XGmd3wcyDg8&feature=youtu.be&t=1071
48 views

### Optimization step in Apprenticeship Learning via Inverse Reinforcement Learning

Why the optimization step of the algorithm a quadratic program? [See: Apprenticeship Learning via Inverse Reinforcement Learning; page 3] Isn't the objective function linear? Why don't we treat ...
27 views

### Simple question about HS algorithm's formul(Optical flow)

In the below pic, I can not understand what U vector is? It says flow field but I can not imagie what really is the flow field?
76 views

### How does this sigma work?(Harris algorithm) [closed]

May someone explains some first iterations of this sigma? Also, how did it convert the above expression to below expression? What it the meaning of I(x) and I(y)?