# Questions tagged [math]

For questions about mathematics related to artificial intelligence.

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48 views

### How to understand mapping function of kernel?

For a kernel function, we have two conditions one is that it should be symmetric which is easy to understand intuitively because dot products are symmetric as well and our kernel should also follow ...
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### What are the variables used in a Gaussian radial basis kernel in the context of SVMs?

If I have the Gaussian kernel $$k(x, x') = \operatorname{exp}\left( -\| x - x' \|^2 / 2\sigma^2 \right)$$ What is $x$ and $x'$ in the context of training an SVM?
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### 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 ...
233 views

### In the context of importance sampling ratio, how is the equation $\mathbb{E}\left[\rho_{t: T-1} G_{t} | S_{t}=s\right]=v_{\pi}(s)$ derived?

When reading the book by Sutton and Barto, I came across the importance sampling ratio. The first equation, I believe, describes the probability a particular sequence is obtained given the current ...
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### 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 ...
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### 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)?
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### Reason for relaxing limit in derivative in this context?

Consider the following paragraph from NUMERICAL COMPUTATION of the deep learning book.. Suppose we have a function $y = f(x)$, where both $x$ and $y$ are real numbers. The derivative of this function ...
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### How to calculate the gradient penalty proposed in "Improved Training of Wasserstein GANs"?

The research paper titled Improved Training of Wasserstein GANs proposed a gradient penalty in order to avoid undesired behavior due to weight clipping of the discriminator. We now propose an ...
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### What is meant by an axis of a tensor?

Tensor is an ordered collection of elements. The elements are generally real numbers. Tensors are used in deep learning for storing data. There is a wide usage of the word "axis" related to ...
123 views

### What is Bayes' theorem?

What is Bayes' theorem? How does it relate to conditional probabilities?
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### In this paper, if region $R_{2}$ moves in a sliding window manner, won't the saliency map have a smaller size than the original image?

In the paper Salient Region Detection and Segmentation, I have a question pertaining to section 3 on the convolution-like operation being performed. I had already asked a few questions about the paper ...
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### Isssue in understanding the derivation regarding mean squared error

The following derivation is taken from Chapter 5: Machine Learning Basics from the book titled Deep Learning (by Aaron Courville et al.) I am facing difficulty in understanding the zero derivative ...
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### What are the Calculus books recommended for begineer to advanced researchers in artificial intelligence?

Calculus is a branch of mathematics that deals with the rate of change of outputs of a function w.r.t the inputs. It contains several concepts including limits, first-order derivatives, higher-order ...
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### How to interpret the policy gradient expression in reinforcement learning?

I'm currently going through the OpenAI's spinning up introduction course to reinforcement learning. On one of the final sections, they derive an expression for the gradient of the undiscounted return ...
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### What's the difference between a 1d tensor and a 2d tensor with 1 dimension?

I'm doing a TensorFlow tutorial, where they convert an array of the numbers [1,2,3] to a tensor like this: ...
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### Do the rows of the design matrix refer to the observations or predictors?

I attempt to understand the formulation of dictionary learning for this paper: Depression Detection via Harvesting Social Media: A Multimodal Dictionary Learning Solution Multimodal Task-Driven ...
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### Mathematical calculation behind decision tree classifier with continuous variables

I am working on a binary classification problem having continuous variables (Gene expression Values). My goal is to classify the samples as case or ...
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### Why are all weights of a neural net updated and not just the weights of the first layer

Why are all weights of a neural net updated and not only the weights of the first hidden layer? The error-influence of the prediction by the weights of a neural net is calculated using the chain rule....
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### How to understand the average l2 loss?

In the snippet below, the highlighted part is the average norm, but since $1/|p_i|$ is outside the summation, it is very confusing to understand. is $|p_i|$ l2-norm(as per wolfram) or l1-norm or ...
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### Notations and definitions relative to distributional reinforcement learning [closed]

I am reading the paper A Distributional Perspective on Reinforcement Learning, Marc G. Bellemare et al. The vague notation in this paper is very annoying. I searched several papers to solve this ...
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### What's wrong with my understanding of how RNNs work?

Recently, I've been trying to derive the mathematics behind various Neural Network structures. I managed to derive the MLP and tested it to be on par with a Keras implementation (Using the MNIST ...