# Questions tagged [math]

For questions about mathematics related to artificial intelligence.

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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 ...
224 views

### Formal proof that every purely reactive agent has behaviorally equivalent standard agent

It kind of makes sense intuitively but I'm not sure about a formal proof. I'll start with briefly listing definitions from Intro to Multiagent systems, Wooldridge, 2002 and then give you my reasoning ...
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### Educational Resources and Programming Languages for AI & ML [closed]

I am a Mathematics graduate who is interested in AI and Machine Learning. I would like to dig deep into the maths of them but I do not know where to start. It seems Linear Algebra is the most crucial ...
57 views

### Why don't integrated gradients explain samples correctly?

I have a linear tabular dataset made of floats. The dataset follows a simple rule like: ...
21k 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 ...
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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 ...
84 views

### Given an axis-angle rotation vector, how can I find the unit rotation axis and angle?

I have a robotics assignment, which I am unable to solve. Given the axis-angle rotation vector $\Theta = (2, 2, 0)$, how can I calculate the unit vector of the rotation axis $k$ and the angle $\theta$?...
14 views

### About the proper method to make some mathematical model from AI trained Weights (Parameters)

If possible, I like to know about the available methods for creating the summarized mathematical models from the trained AI weights. For example, I need to make some summarized model from the trained ...
23 views

### Is there any closed form analytical expression to represent fractional max pooling?

There are Nineteen types of pooling layers in PyTorch. Almost all of the layers are provided with corresponding analytical formulae. But analytical formulae are not provided for the fractional max-...
2k views

### Has the Fibonacci series or the golden ratio been applied in any way in AI?

I have been looking at the Fibonacci series, the golden ratio, and its uses in nature, like how flowers and animals grow based on the series. I was wondering whether we could use the Fibonacci series ...
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### REINFORCE differentiation on sum or single value?

I'm currently learning Policy-gradient Methods for RL and encountered REINFORCE algorithm. I learned from this site : https://towardsdatascience.com/policy-gradient-methods-104c783251e0 that the ...
77 views

### Why can a neural network use more than one activation function?

From trying to understand neural networks better, I've come upon a tentative notion that an activation function aims to build a function it's approximating via linear combinations with biases and ...
22 views

### Is the range of inception score flexible or bounded based on number of classes?

Inception score is used to evaluate the generative models. It is a score given based on quality and diversity of images generated. I have doubt about the range of inception score because of the reason ...
66 views

### 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 ...
23 views

### What are the different types of geometry in literature that may be used for deep learning?

Recently, I asked a question on the concept of a manifold and received an answer that points to a relatively new subfield of deep learning named geometric deep learning. In the ...
30 views

### What should the value of $ρ$ in the $w(n+1) = w(n) + \rho*\text{error}(i)x(i)$ formula of Least Mean Squares be?

I am trying to better understand the Least Mean Squares algorithm, in order to implement it programmatically. If we consider its weight updating formula $$w(n+1) = w(n) + \rho * \text{error}(i)x(i),$$ ...
36 views

### What are mathematically the factors of variation in deep learning?

The following paragraph from an answer tells us about factors of variation Factors of variation are some factors which determine varieties in observed data. If that factors change, the behaviour of ...
31 views

### What is meant by "well-behaved gradient" in this context?

Consider the following statement about the success of discriminative models So far, the most striking successes in deep learning have involved discriminative models, usually those that map a high-...
118 views

### What is Lipschitz constraint and why it is enforced on discriminator?

The following is the abstract for the research paper titled Improved Training of Wasserstein GANs Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training ...
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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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### Why not undefined expression is different from numerical underflow?

Consider an architecture or programming language that uses $n$ bits for storing a floating point number in a particular format. Then each and every floating point number it can store should be in a ...
33 views

### 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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### Is it true that real world data is highly discontinuous?

A function $f$ is said to be continuous at a point $c$ if it satisfies three properties: Should be defined at the point $c$ Left and right-hand limits at $c$ must be equal i.e., the limit must exist ...
99 views

### Is there any domain in machine learning that solves a problem by using only analytical algorithms?

Most of the algorithms in machine learning I am aware of use datasets and learning happens in an iterative manner given some examples. The examples can also be understood as experience in the case of ...
229 views

### Defining formula for fuzzy equation

I'm learning fuzzy logic and more or less understand the basic concept, but i'm having a hard time understanding how to apply it to a method. I tried browsing online for explanation on how to use it, ...
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### Is there any geometrical interpretation on overcoming gradient related problems by adjusting/changing loss function?

There are instances in literature where we need to change loss function in order to escape from gradient problems. Let $L_f$ be a loss function for a model I need to train on. Some times $L_f$ leads ...
331 views

### In a single neuron output layer should the output be a scalar?

Given a neural network with 3 inputs, 4 hidden layers, and 1 output, should the output neuron be a vector or a scalar? I thought that at the end of the summation only one number between 0 and 1 would ...
14 views

### A 2D distance measure that gives weightage to the angle between the two points?

n1 n8 n7 n2 c n6 n3 n4 n5 Assume that all neighbors ni are (Euclidean) ...
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### What are the iid random variables for a dataset in the GAN framework?

I am trying to understand why mean is used for expectation in training Generative Adversarial Networks. The answer tells that it is due to the law of large numbers which is based on the assumption ...
90 views

### 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 ...
32 views

### 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 ...
63 views

### 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 ...
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### What math should I learn before and while using and applying deep learning?

I want to learn deep learning. After researching a little, I came to the conclusion that I need a lot of math. I've started a linear algebra course, and it takes a long time (2-3 weeks). I want to ...
57 views

### What are the necessary mathematical properties to be a loss function in gradient based optimizations?

Loss functions are used in training neural networks. I am interested in knowing the mathematical properties that are necessary for a loss function to participate in gradient descent optimization. I ...
72 views

### Questions about a research paper on salient region detection and segmentation

I am reading this paper in an attempt to recreate the salient region detection and segmentation model employed. I have the following questions pertaining to section 3 of the paper and I would highly ...
32 views

### How can I compute a mathematical formula for my CNN?

Let's say, for example, I have built the following CNN model using Keras: ...
69 views

### Is it possible to know the distance objects are from camera based on only knowing one object's height?

I am doing a project where I have to know distance a particular object is from camera. In the photo I only know one of the object's height, but I don't know how far away that object is and I don't ...
32 views

### 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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### Why is tanh a "smoothly" differentiable function?

The sigmoid, tanh, and ReLU are popular and useful activation functions in the literature. The following excerpt taken from p4 of Neural Networks and Neural Language Models says that ...
Consider a dataset with $n$ training examples and $d$ features. Let $D_{n \times d}$ be the data matrix and $r$ be the rank of it. In matrices, rank $r$ is generally useful in Knowing the dimension ...