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For questions about mathematics related to artificial intelligence.

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Showing Axis-Aligned Rectangles With Noise Are PAC-Learnable (FML, Problem 2.6)

I asked the following in Math Stack Exchange and was told "You may be more likely to get an answer on stats.stackexchange.com". I figured this is a more suitable place. In what follows, an ...
Choripán Con Pebre's user avatar
1 vote
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45 views

Why doesn't the Kolmogorov-Arnold representation theorem imply an MLP-like structure?

Recently, Kolmogorov-Arnold Networks (KANs) generated a lot of hype, with "AI experts" throwing around terms like "ML 2.0" and "a new era of ML". KANs are supposedly ...
ihatejetsons's user avatar
1 vote
0 answers
42 views

Why is policy gradient theorem so important?

What is the problem that the policy gradient solves? From what I understand the problem is taking the gradient of the state distirbution $d^{\pi_{\theta}}$, but what is exactly the problem here (maybe ...
craaaft's user avatar
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AI capable of mathematical creation? (reference request)

I was studying philosophy of AI when a question came to my mind. I'd like to write an essay (both informative and argumentative) about the state of the art in Artificial Intelligence advancing the ...
Amanda Wealth's user avatar
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7 views

How to quantify the impact of tokenizer output changes on text encoder embeddings?

In natural language processing, generating text embeddings involves two key modules: the tokenizer and the text encoder. The tokenizer converts text into a token vector, which the encoder then uses to ...
hanugm's user avatar
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Need some feedback on an idea for using reinforcement learning in the context of medical imaging reconstruction

Disclaimer -- this idea may be totally half-baked, I'm not sure. I have used deep learning models in image reconstruction before (and this is a super hot topic in the field right now), but only in the ...
t_h's user avatar
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1 answer
33 views

Could AlphaZero be trained to prefer "beautiful" games?

Could a version of AlphaZero be trained that learned not only how to win, but how to win in a "beautiful" way? Jurgen Schmidhuber wrote a paper in 2008, which basically models "beauty&...
swami's user avatar
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How is pass@k metric defined for automated theorem provers if we have a verifier?

The pass@k metric was proposed to measure the percentage of successful code samples (https://arxiv.org/abs/2107.03374), but it has also been used in automated theorem proving such as https://arxiv.org/...
user131379's user avatar
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Is it reasonable to ask for the same time-regularity of the high and low dimensional signals?

Consider we are dealing with sequential data sampled from a continuous time signal $x(t)\in \mathbb{R}^n$, so that the dataset will look like $\{x_0,x_1,…,x_n\}$, with $x_i= x(t_i)$. Assume that we ...
user8354084's user avatar
2 votes
1 answer
129 views

Neural Networks are universal approximators? - Exercice 20.1 UML

I'm working on this question which can be found at page 282 of "Understanding Machine Learning: From Theory to Algorithms" by Shai Shalev-Shwartz and Shai Ben-David. The statement is as ...
mabed's user avatar
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Implications of Not Zero-Centering Data in Diffusion Models: Impact on Performance and Stability?

I've been exploring the implementation and theory behind diffusion models, particularly in how they manage the latent space. A recurring theme is the emphasis on zero-centering the latent space and ...
Voyager's user avatar
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3 votes
2 answers
83 views

How does diffusion based text-to-image generation models Mathematically classify inputs to outputs?

I've been exploring the capabilities of the Diffusion based text-to-image models and am curious about its underlying mathematical framework. Specifically, I'm interested in understanding how the model ...
hanugm's user avatar
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Solving an ODE with factors that span over orders of magnitude in the region of interest with PINN

I am trying to solve the following ordinary differential equation (ODE) with a physics informed neural network (PINN) $$ \frac{dZ}{dx} = A(x) (1-Z^2) \exp(-Z) - B(x) $$ where A(x) function varies in ...
Maxim's user avatar
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1 answer
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What is the matrix representation of a dilated convolution?

I am delving into the matrix representation of dilated convolutions, especially after understanding standard 1D convolutions as Toeplitz matrix-vector multiplications. My specific focus is on Dilated ...
Yanirmr's user avatar
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What is the name of this construction for a compound policy that operates over distinct action sets?

I am developing an RL algorithm with a policy that needs to compute valid probabilities over multiple distinct action sets. I think I have a construction that will work, but I do not know what it is ...
Wowee's user avatar
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What is the meaning of "energy loss" in PCA?

Recently in a slide in about PCA (Principal Component Analysis) I saw a question: "How much is the data energy loss in PCA?&...
hasanghaforian's user avatar
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Neural networks with a continuous function as the input

I am rethinking image recognition algorithms, and want to use an idea I saw in a 3Blue1Brown video: The basic idea is to map pixels on an image to a specific frequency—every point is distinct—and if ...
Ank i zle's user avatar
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Finding resulting domains after enforcing arc consistency

This question is about the below exam scheduling constraint satisfaction graph, where each node represents a course. Each course is associated with an initial domain of possible exam days (most ...
Koduko's user avatar
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Is there a database of math conversations with Chat GPT?

I would like to make GPT (or other AI Chat, if someone knows better) to assist me in my mathematical education. But hard to say what GPT is capable to do. Some testing tasks are performed well by him, ...
Widawensen's user avatar
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DDPM - why after adding gaussian noise to image, we assume that new image is from normal distribution?

I have a question about forward process in DDPM. It is described as we sample our image from some distribution: $x_0\sim{q(x)}$ then in each time stamp $T$ we are applying gaussian noise $\epsilon\sim\...
cvzx's user avatar
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What kind of learning architecture can I use to solve a set of nonlinear thermodynamic equations?

I am in the business of solving equations based in thermodynamics. Technically speaking, I am trying to solve for the binodals for a ternary system. The binodal is a curve in a phase diagram. ...
bad_chemist's user avatar
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0 answers
70 views

claude 2 doesn't know basic math? [duplicate]

Sometimes, when I see answers like this from large language models, it makes me feel disgusted: Me: Does Voyager 1 have enough velocity to escape the solar system without using Jupiter's gravity ...
Mr Saw's user avatar
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Is it possible tofind a subset of F_p for large p such that no solutions exist

I'm aware that neural networks are probably not designed to do that, however asking hypothetically: I have a question regarding the possibility of identifying a subset of $\mathbb{F}_p$ in which a ...
laura's user avatar
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2 votes
1 answer
308 views

Why can AI not understand numbers- even basic ones? [duplicate]

I asked Bard to "Give me a challenging mathematical riddle to which the answer is 23" It answered: "Here is a challenging mathematical riddle to which the answer is 23: I am the sum of ...
ben svenssohn's user avatar
-2 votes
2 answers
64 views

Size of a neural network [closed]

For any type of ANN, is there a common formula which can be used to calculate size of a neural network?
Indika Alahapperuma's user avatar
3 votes
3 answers
2k views

What will happen if to train an LLM on mathematical exersises?

What will happen if to train an LLM on taking integrals and solving equations? The process of mathematical education can be absolutely automated by a computer algebra system because the verification ...
Anixx's user avatar
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0 answers
33 views

Understanding the decreasing influence of text embedding in Text-to-Image diffusion models: A Mathematical perspective

I've been reading the paper titled eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoisers by Yogesh Balaji et. al. Consider the following excerpt from the abstract of the paper ...
hanugm's user avatar
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-1 votes
1 answer
40 views

Sum of gaussian distribution [closed]

I assume the sum of the Gaussian distribution is 1. However, the actual calculation in JavaScript yields a value greater than 1 in JavaScript. Is this code wrong? gaussian_distribution.html] ...
diffusion stable's user avatar
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1 answer
252 views

Can neural-networks solve a system of non-linear algebraic equation

I am currently doing research as a PhD student in theoretical physics. Currently we are calculating physical quantities described by coupled non-linear algebraic systems of equations. These equations ...
SaFeHe's user avatar
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107 views

RetNet: Why Diagonalize A Square Matrix?

The paragraph before eq. (3) in The RetNet paper says to diagonalize the $R^{d{\times}d}$ matrix $A$. I am confused as to why one would not just use a vector? One of the arguments that I have heard on ...
Umar Siregar's user avatar
1 vote
0 answers
38 views

Can a Fully Connected Neural Network represent all Neural Networks of smaller size?

A fully connected Neural Network architecture can be characterized by a vector $\mathbf a = (a_0,a_1,\ldots,a_L)\in\mathbb N^{L+1}$ and an activation function $\sigma :\mathbb R\to\mathbb R$. In this ...
Stratos supports the strike's user avatar
1 vote
1 answer
36 views

How do we get from types of activation functions to fitting lines to our data?

I'm completely new to AI and admittedly have never been good at math (also please excuse me if I use the wrong terminology). Despite this, I'm trying wrap my head around activation functions and how ...
Garrett's user avatar
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2 answers
84 views

How is speech recognition software able to distinguish between different speakers and yet still understand them all?

Some background: I'm an EE major and data science minor, so I have a basic understanding of machine learning - I had a one semester course on it where we covered some of the most commonly used ...
Mikayla Eckel Cifrese's user avatar
0 votes
1 answer
154 views

Machine Learning Math Requirements [duplicate]

What area of math do i need for AI and ML? and some recommendations for YouTube math's playlist I've just started to learn to code in python and i want to go to the path of AI/ML
Kenezzu Len's user avatar
0 votes
1 answer
149 views

How are the intuitions and mathematics of attention mechanisms related to those of PageRank?

Excuse me if you find this question too vague and not fitting to this forum and feel free to close it. The overall goal of my question is to get a better intuition of the attention concept and ...
Hans-Peter Stricker's user avatar
2 votes
1 answer
86 views

Is the problem of Language Modelling a Well-Posed Learning Problem?

Hadamard defines (Well-posed problem (Wikipedia)) a well-posed problem as one for which: a solution exists, the solution is unique, the solution depends continuously on the data (e.g. it is stable) ...
aren't eistert's user avatar
1 vote
1 answer
908 views

What operation is ggml_mul_mat performing? (K×Q in LLaMA)

I’m reading the source code of alpaca.cpp in an attempt to understand how a large language model works. (I have a strong programming background, but almost no math, ...
Wolfgang's user avatar
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1 vote
0 answers
27 views

Is Machine learning a good approach for this geometric challenge?

For months I have been working on a conventional algorithm that positions circles with different sized radii and either positive or negative charge within an outer radius in such a way that the charge ...
Vale's user avatar
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3 votes
0 answers
187 views

Best calculus books for Deep Learning

Recommend some calculus books for Deep Learning and neural networks. I know what is integration, differentiation, derivates, limits on a based level. I would like to understand on deep level the ...
Dan Il's user avatar
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1 vote
1 answer
113 views

Is there a mathematical proof that a binary neural network can approximate any function with arbitrary accuracy?

Since the Universal approximation theorem shows that standard multilayer feedforward networks with as few as a single hidden layer, sufficient hidden units, and arbitrary bounded and nonconstant ...
user68072's user avatar
1 vote
0 answers
48 views

Computation required for GPT model to choose likely word from n-options where n < total vocabulary size

Let’s imagine two different use cases for a LLM/GPT-3. Predicting the next most likely word in a sequence using all ~50k words in its dictionary (i.e. the standard method of prompting a LLM) Checking ...
Derek's user avatar
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3 votes
1 answer
668 views

What exactly is the future of mathematical analysis that can be dealt with AI (especially in the automated theorem proving)?

As a student of numerical analysis, I can see how mathematical analysis involved in making a language program specifically in the convergence analysis of an approximation method. But, while chatting ...
Messi Lio's user avatar
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0 votes
1 answer
127 views

How much pure math should I know for deep learning? [duplicate]

Recently I've been wondering about the necessary amount of math that a deep learning scientist really needs to know. From what I could gather around the internet there are 3 big areas(calculus 1,2 and,...
Tom PL's user avatar
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0 votes
1 answer
34 views

Is $i$ indexing the first or second dimension in $\mathbf{x}_i$, where $\mathbf{x} \in \mathbb{R}^{n\times d}$?

I was reading the following notes on the math behind transformers and was confused about what $\mathbf{x}_i$ is? If $\mathbf{x} \in \mathbb{R}^{n\times d}$, then is the $i$ indexing the $n$ or the the ...
play's user avatar
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1 vote
1 answer
42 views

What does this bracket notation $\langle\phi(x),v\rangle$ mean?

I found it at the bottom of page 2 of the paper Intriguing properties of neural networks (2014), in the form of $$\underset{x\in\mathcal{I}}{\mathrm{arg\,max}}\langle\phi(x),v\rangle$$
Nils André's user avatar
29 votes
4 answers
36k views

Why is ChatGPT bad at math?

As opposed to How does ChatGPT know math?, I've been seeing some things floating around the Twitterverse about how ChatGPT can actually be very bad at math. For instance, I asked it "If it takes ...
Mithical's user avatar
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24 votes
4 answers
12k views

How does ChatGPT know math?

ChatGPT is a language model. As far as I know and If I'm not wrong, it gets text as tokens and word embeddings. So, how can it do math? For example, I asked: ME: Which one is bigger 5 or 9. ChatGPT: ...
Peyman's user avatar
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2 votes
2 answers
233 views

Where does the proximal policy optimization objective's ratio term come from?

I will use the notation used in the proximal policy optimization paper. What approximation is needed to arrive at the surrogate objective (equation (6) above) with the ratio $r_t(\theta)$? Put ...
fool's user avatar
  • 203
1 vote
1 answer
375 views

Interpretation of the Dynamic Time Warping (DTW) graph

How can I interpret ate the DTW graph. I understood the algorithm behind DTW, but I struggle to interpret ate the graph. When I compute the DTW for a signal that is the same signal but shifted in time,...
Skobo Do's user avatar
2 votes
1 answer
1k views

Are my proofs that the Bellman operators are contractions correct?

Introduction I'm studying Reinforcement Learning, and in order to increase my understanding I've been challenging myself by trying to write proofs that show that the right hand side of the Bellman ...
cfml's user avatar
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