Questions tagged [math]

For questions about mathematics related to artificial intelligence.

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46 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: ...
13 views

Are there any good references that describe the equations of the forward pass of Graph Neural Networks?

I am trying to program Graph Neural Network from scratch. Can the community please suggest a good reference/s to read about the equations of the forward pass in Graph Neural Networks, especially in ...
128 views

Why do we use the word “kernel” in the expression “Gaussian kernel”?

I've heard the expression "Gaussian kernel" in several contexts (e.g. in the kernel trick used in SVM). A Gaussian kernel usually refers to a Gaussian function (that is, a function similar to the ...
17 views

(Deep) feature engineering for lambda terms (mathematical expressions, higher order logic formulas) - is such thing?

Automated theorem proving with (deep) reinforcement learning (DRL) approach is hot topic in current AI research when domains of games are becoming saturated and completed research topcis. E.g. there ...
72 views

Is it okay to think of any dataset in artificial intelligence as a mathematical set?

A dataset is a collection of data points. It is known that the data points in the dataset can repeat. And the repetition does matter for building AI models. So, why does the word dataset contain the ...
77 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 $\theta$?...
85 views

Can a computer make a proof by induction?

Can a computer solve the following problem, i.e. make a proof by induction? And why? Prove by induction that $$\sum_{k=1}^nk^3=\left(\frac{n(n+1)}{2}\right)^2, \, \, \, \forall n\in\mathbb N .$$ I'm ...
30 views

how to go from mathematical problem to neural network (and back)?

I am a little confused on how, you can find online papers that describe complex Machine Learning formulas in a mathematical/probabilistic way, and, in the other hands, easy tutorials that teach you ...
60 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 ...
158 views

918 views

Can we get the inverse of the function that a neural network represents?

I was wondering if it's possible to get the inverse of a neural network. If we view a NN as a function, can we obtain its inverse? I tried to build a simple MNIST architecture, with the input of (784,...
61 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 ...
507 views

What is the fundamental difference between an ML model and a function?

A model can be roughly defined as any design that is able to solve an ML task. Examples of models are the neural network, decision tree, Markov network, etc. A function can be defined as a set of ...
198 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 ...
82 views

Can we use ML to do anything else other than predicting (in the case of mathematical problems)?

(The math problem here just serves as an example, my question is on this type of problems in general). Given two Schur polynomials, $s_\mu$, $s_\nu$, we know that we can decompose their product into a ...
4k views

What are the mathematical prerequisites to be able to study artificial general intelligence?

What are the mathematical prerequisites to be able to study artificial general intelligence (AGI) or strong AI?
75 views

How do you calculate KL divergence on a three-dimensional space for a Variational Autoencoder?

I'm trying to implement a variational auto-encoder (as seen in Section 3.1 here: https://arxiv.org/pdf/2004.06271.pdf). It differs from a traditional VAE because it encodes its input images to three-...
54 views

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 ...
100 views

What is the meaning of the words 'bias' and 'variance' in RL?

In reinforcement learning approaches, like temporal-difference (TD) learning or Monte Carlo methods, two of the metrics used to measure their performance are the bias and the variance. What do these ...
2k views

What sort of mathematical problems are there in AI that people are working on?

I recently got a 18-month postdoc position in a math department. It's a position with relative light teaching duty and a lot of freedom about what type of research that I want to do. Previously I was ...
164 views

Mathematical foundations of the ability to learn

I am an undergraduate student in applied mathematics with an interest in artificial intelligence. I am currently exploring topics where I could do research. Coming from a mathematical background I am ...
71 views

How to compute the gradient of the cross-entropy loss function with respect to the parameters with softmax activation function?

I've seen plenty of examples of people doing Sigmoid + MSE backpropagation implementations, yet I do not seem to understand how to implement backpropagation as stated in the title in the case of multi-...
16 views

Is parameter sharing in AlBERT akin to repeated application of same function on input?

I read the AlBERT and saw that its architecture used "Parameter Sharing" among layers of the encoder. They mentioned that this was done to save model space, make fewer training parameters ...
228 views

How does the forget layer of an LSTM work?

Can someone explain the mathematical intuition behind the forget layer of an LSTM? So as far as I understand it, the cell state is essentially long term memory embedding (correct me if I'm wrong), ...
120 views

What does the formula $1-\sum_i(e_i-a_i)^2$ mean in this NEAT Python API?

I have looked at the documentation for the NEAT Python API found here, where it's written The error for each genome is $1-\sum_i(e_i-a_i)^2$ I have not yet learned calculus, so I can't understand ...
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What is $\nabla_{\theta_{k-1}} \theta_{k}$ in the context of MAML?

I am attempting to fully understand the explicit derivation and computation of the Hessian and how it is used in MAML. I came across this blog: https://lilianweng.github.io/lil-log/2018/11/30/meta-...
118 views

Why is my derivation of the back-propagation equations inconsistent with Andrew Ng's slides from Coursera?

I am using the cross-entropy cost function to calculate its derivatives using different variables $Z, W$ and $b$ at different instances. Please refer image below for calculation. As per my knowledge, ...