ChatGPT, Myths and Realities

Everything you wanted to know about Deep Learning but were afraid to ask

Tanguy Lefort

tanguy.lefort@umontpellier.fr

Université de Montpellier, IMAG

CNRS, Inria, LIRMM

François-David Collin

francois-david.collin@umontpellier.fr

CNRS

IMAG

2024-02-01

ChatGPT, Myths and Realities

Generalities on Machine Learning and Artificial Intelligence

Historical perspective timeline

1950s: perceptron (Rosenblatt 1958)
1960s: perceptron convergence theorem (Minsky and Papert 1969)
1970s-1980s: backpropagation (Rumelhart, Hinton, and Williams 1986)
1990s: SVM (Cortes and Vapnik 1995)
2000s: Boosting (Freund and Schapire 1997), Random Forests (Breiman 2001)
2010s: Deep Learning (Goodfellow, Bengio, and Courville 2016)

AI domains

Artificial Intelligence (AI)

Machine Learning (ML)

Deep Learning (DL)

Large Language Models (LLM)

Train a neural network

Training a supervised Machine learning model

Class of prediction functions f_\theta: linear, quadratic, trees
Loss \mathcal{L}: L^2 norm, CrossEntropy, purity score
Optimizer: SGD, Adam, …
- learning rate \eta: \theta_{k+1} \gets \theta_k - \eta \nabla_\theta \mathcal{L}
- other hyperparameters
Dataset:
- training: \{(x_i, y_i)\}_{i} to compute loss between prediction f_{\theta}(x_i) and label y_i to update \theta
- test: only compute performance scores (no more updates !)

A quick survey of Deep Learning

Foreword, beware the Alchemy

More or less theoretical guarantees
- field of research
- type of network
- from theory to applications: a gap
Myriad of ad-hoc choices, engeenering tricks and empirical observations
Current choices are critical for success: what are their pros and cons?
Try \rightarrow Fail \rightarrow Try again is the current pipeline

Science and/or Alchemy?

Criticable current state of Deep Learning research,
lack of scientific rigor in the field.

Vigorous response from Y. LeCun and his “followers”

arguing that mathematical rigor is not critical in Deep Learning research
the field is doing just fine without it.

Criticizing an entire community (and an incredibly successful one at that) for practicing “alchemy”, simply because our current theoretical tools haven’t caught up with our practice is dangerous. Why dangerous? It’s exactly this kind of attitude that lead the ML community to abandon neural nets for over 10 years, despite ample empirical evidence that they worked very well in many situations. (Yann LeCun, 2017, My take on Ali Rahimi’s “Test of Time” award talk at NIPS.)

The main ingredients

Tensor algebra (linear algebra)
Automatic differentiation
(Stochastic) Gradient descent
Optimizers
Non-linearities
Large datasets

Also, on hardware side:

GPU
Distributed computing

shape=(batch, height, width, features)

Tensor algebra

Linear algebra operations on tensors
MultiLayerPerceptron = sequence of linear operations and non-linear activations

\Rightarrow input can be anything: images, videos, text, sound, …

Automatic differentiation

chain rule to compute gradient with respect to \theta
key tool: backpropagation
- don’t need to store the computation graph entirely
- gradient is fast to compute (a single pass)
- but memory intensive

f(x)=\nabla\frac{x_{1}x_{2} sin(x_3) +e^{x_{1}x_{2}}}{x_3}

\begin{darray}{rcl} x_4 & = & x_{1}x_{2}, \\ x_5 & = & sin(x_3), \\ x_6 & = & e^{x_4}, \\ x_7 & = & x_{4}x_{5}, \\ x_8 & = & x_{6}+x_7, \\ x_9 & = & x_{8}/x_3. \end{darray}

Gradient descent

Example with a non-convex function

Plotly = require('plotly.js-dist');

f(x_1, x_2) = (x_1^2 + x_2 - 11)^2 + (x_1 + x_2^2 - 7)^2

minX = -5;
maxX = 5;

f = ([x1, x2]) => (x1**2 + x2 - 11)**2 + (x1 + x2**2 - 7)**2;

{
  const linspace = d3.scaleLinear().domain([0, 49]).range([minX, maxX]);
  const X1 = Array.from({length: 50}, (_, i) => linspace(i));
  const X2 = Array.from({length: 50}, (_, i) => linspace(i));

  // Define your function f here
  const f = ([x1, x2]) => (x1**2 + x2 - 11)**2 + (x1 + x2**2 - 7)**2;

  const Z = X1.map((x1,i) => X2.map((x2,j) => f([x1,x2])));

  const data = [{
    x: X1.flat(),
    y: X2.flat(),
    z: Z,
    type: 'surface'
  }];

  const layout = {
    title: '',
    autosize: false,
    width: 500,
    height: 500,
    paper_bgcolor: "rgba(0,0,0,0)",
    plot_bgcolor: "rgba(0,0,0,0)",
    template: 'plotly_dark',
    margin: {
      l: 65,
      r: 50,
      b: 65,
      t: 90,
    }
  };

  const div = document.createElement('div');
  Plotly.newPlot(div, data, layout,{displayModeBar: false});
  return div;
}

function grad_descent(x1,x2,step,max_iter) {
  let grad = f_grad(x1, x2);
  let iterations = [[x1, x2]];
  function f_grad(x1, x2) {
    let df_x1 = 2 * (-7 + x1 + x2**2 + 2 * x1 * (-11 + x1**2 + x2));
    let df_x2 = 2 * (-11 + x1**2 + x2 + 2 * x2 * (-7 + x1 + x2**2));
    return [df_x1, df_x2];
  }
  var count = 0;
  while (count < max_iter) {
    x1 -= step * grad[0];
    x2 -= step * grad[1];
    grad = f_grad(x1, x2);
    if (isFinite(x1) && isFinite(x2) &&
      (minX < x1) && (x1 < maxX) &&
      (minX < x2) && (x2 < maxX))
        iterations.push([x1, x2]);
    else iterations.push(iterations[count])
    count += 1
  }
  return iterations;
}

viewof descent_params = Inputs.form({
  x1: Inputs.range([minX, maxX], {step: 0.1, value: 0, label: 'x1'}),
  x2: Inputs.range([minX, maxX], {step: 0.1, value: 0, label: 'x2'}),
  step: Inputs.range([0.001, 0.04], {step: 0.001, value: 0.01, label: 'step_size'})
})

{
  var iterations = grad_descent(descent_params.x1,descent_params.x2,descent_params.step,20)
  return Plot.plot({
    aspectRatio: 1,
    x: {tickSpacing: 50, label: "x1 →"},
    y: {tickSpacing: 50, label: "x2 →"},
    width: 400,
    style: {
      backgroundColor: 'rgba(0,0,0,0)'
    },
    marks: [
      Plot.contour({
        fill: (x1, x2) => Math.sqrt((x1**2 + x2 - 11)**2 + (x1 + x2**2 - 7)**2),
        x1: minX,
        y1: minX,
        x2: maxX,
        y2: maxX,
        showlegend: false,
        colorscale: 'RdBu',
        ncontours: 30
      }),
      Plot.line(iterations,{marker: true})
    ]
  })
}

Sensitivity to initial point and step size

(Stochastic) Gradient descent

not use all the data at once to compute the gradient
- not feasible in practice (memory wise)
Use mini-batch of data (boostrap samples)
- one more hyperparameter…

\theta_{k+1} \leftarrow \theta_k - \frac{\eta}{n}\sum_{i\in\text{batch}}\nabla_\theta \mathcal{L}(f_\theta(x_i), y_i)

\Rightarrow No general guarantees of convergence in DL setting

Optimizers

SGD, Adam, RMSProp

Non-convex optimization research on the subject is still very active, and there is no clear consensus on what is the best optimizer to use in a given situation.
No guarantee of global minimum, only local minimum
No guarantee of convergence, only convergence in probability

(More than) a pinch of non-linearities

Linear Transformations + Non-linear activation functions
radically enhance the expressive power of the model
ability to explore the space of functions in gradient descent.

Train a Large Language Model (LLM)

From text to numbers

Main problem: we can’t multiply or do convolutions with words
Second problem: many words (for a single language)
Third problem: how to capture semantics?

Embeddings

Distance between words should not be character based

women

woman

window

widow

Embeddings

Distance between words should not be caracter based

widow

women

woman

window

BERT: Bidirectional Encoder Representations from Transformers

embeddings: represent words as vectors in high dimensions

An example

“We need to book a flight, and we need a book to pass time, also book an hotel!”

[CLS]           101
we            2,057
need          2,342
to            2,000
book          2,338
a             1,037
flight        3,462
,             1,010
and           1,998
we            2,057
need          2,342
a             1,037
book          2,338
to            2,000
pass          3,413
time          2,051
,             1,010
also          2,036
book          2,338
an            2,019
hotel         3,309
!               999
[SEP]           102

First 5 vector values for each instance of "project".

book a flight:    tensor([ 2.7359, -6.4879,  0.6554,  0.4170,  6.0187])
need a book:   tensor([ 3.3611,  1.1988,  3.2118, -0.8919,  5.3709])
book an hotel:    tensor([ 3.2382, -0.8284,  1.4804, -0.7448,  5.4106])

Vector similarity for  *similar*  meanings:  0.82
Vector similarity for *different* meanings:  0.59

Training ChatGPT

Attention networks in ChatGPT

DL layers = capture different levels of dependencies in the data
multi-head attention mechansim applies “multi-scale learning” to data sequences \Rightarrow e.g. not only words in sentences, but sentences in paragraphs, paragraphs in documents and so on.

Previously, recurrent networks limited in sequential dependencies,

\Rightarrow transformers capture dependencies in the “whole” in parallel (much faster)

Transformers

Vaswani et al. (2017)

Heart of Transformers: Attention mechanism

\text{Attention}(Q,K,V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V

Three matrices: Query, Key, Value, derived from the input sequence
d_k: dimension of the key matrix, typically 64 or 128
we want to compute a weighted sum of the values V with weights given by the compatibility between the query and the keys
softmax to get a probability distribution
multi-head attention: several attention mechanisms in parallel

Vaswani et al. (2017)

Training using humans

pretraining (unsupervised learning): fill blanck, attention mechanisms, next word
fine-tuning (supervised learning): specific dialogues, hyperparameters tuning
RLHF (reinforcement learning): workers give feedback and possible rewards + exploration

@anthrupad

The problem with generating text

Was King Renoit real?

Is King Renoit mentioned in the Song of Roland, yes or no?

Training dataset

very large dataset: (570Gb of text data, 499 B of tokens)

{
  var data = [{
      values: [3, 8, 7, 22, 60],
      labels: ["wikipedia", "Books1", "Books2", "Webtext2", "Common Crawl"],
      textinfo: "label+percent", 
      type: "pie",
      marker: {
          colors: ["lightcyan", "cyan", "royalblue", "darkblue", "gold"]
      }
  }];

  var layout = {
    template: 'plotly_dark',
    paper_bgcolor: "rgba(0,0,0,0)",
    plot_bgcolor: "rgba(0,0,0,0)",
    font: {
        size: 26,
        color: "white"
    },
    margin: {"t": 0, "b": 0, "l": 0, "r": 0},
    showlegend: false
  };

  const div = document.createElement('div');
  Plotly.newPlot(div, data, layout,{displayModeBar: false});
  return div;
}

Repartition of the training dataset

Underrepresentation on the web means less accuracy and more hallucinations!

Other data (chosen quality)
Weighted sampling: Wikipedia=5CommonCrawl, Books1=20ComonCrawl,…

Political and Ecological impacts of Deep Learning/LLMs

Ecological impact

2019: BERT \rightarrowround-trip transcontinental flight for one person
ChatGPT (GPT-3 model):
- electricity used to train: 1,287 MWh and 552 tCO2
  - ~3 private jet flights SF-NY or ~91 french for a year
- daily carbon footprint ~23.04kgCO2 \rightarrow~8.4 tCO2 in a year
  - assuming it runs on 16 A100 GPUs \rightarrowvery low estimation
  - more than the average french for a year
- refreshing data centers for training $$700K liters of freshwater=produce 320 Tesla cars
- a conversation of 20–50 questions = 500mL bottle of freshwater

Training ChatGPT: locations is impactful

leftmost: from Canada / Switzerland to India and West South Africa (x50 factor)

Human considerations

OpenAI outsources check text to Sama (SF company)
Sama employs Kenyan workers (underpaid, toxic content, alienating work)
Denied sessions with wellness counselors
lawsuits in progress with Meta in Nairobi

“Outsourcing trauma to the developing world”

workers are approached in Kibera, the largest informal settlement in Africa
salaries too low to improve their situation, only keep it

Other concerns

biased content and inaccuracies are flooding the internet: no truth only plausible
privacy concerns
plagiarism
copyright infringements: users are responsible in case of litigation not OpenAI

Impactful tool, with limitations and ethical challenges

Concerns on the scientific side

lack of theoretical understanding, trial and error only

\Rightarrow engineering ad-hoc solutions, giant panels of knobs to turn
race to performance impacting reviews quality and content
- stressful for engineers and researchers,
- new jobs appear and disappear with trends
\Rightarrow replacing domain specialists and researchers

Numbers of papers in ArXiv at cs.AI, cs.LG, cs.NE and stat.ML

Krenn et. al 2023

Thank you!

References

Breiman, Leo. 2001. “Random Forests.” Machine Learning 45: 5–32.

Cortes, Corinna, and Vladimir Vapnik. 1995. “Support-Vector Networks.” Machine Learning 20: 273–97.

Freund, Yoav, and Robert E Schapire. 1997. “A Decision-Theoretic Generalization of on-Line Learning and an Application to Boosting.” Journal of Computer and System Sciences 55 (1): 119–39.

Goodfellow, Ian, Yoshua Bengio, and Aaron Courville. 2016. Deep Learning. MIT press.

Jumper, John, Richard Evans, Alexander Pritzel, Tim Green, Michael Figurnov, Olaf Ronneberger, Kathryn Tunyasuvunakool, et al. 2021. “Highly Accurate Protein Structure Prediction with AlphaFold.” Nature 596 (7873): 583–89.

Minsky, Marvin, and Seymour Papert. 1969. “An Introduction to Computational Geometry.” Cambridge Tiass., HIT 479 (480): 104.

Rosenblatt, Frank. 1958. “The Perceptron: A Probabilistic Model for Information Storage and Organization in the Brain.” Psychological Review 65 (6): 386.

Rumelhart, David E, Geoffrey E Hinton, and Ronald J Williams. 1986. “Learning Representations by Back-Propagating Errors.” Nature 323 (6088): 533–36.

Vaswani, Ashish, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. 2017. “Attention Is All You Need.” Advances in Neural Information Processing Systems 30.

Appendix

Large datasets

In machine learning, “overfitting” in the training phase is a concern with a function space too large compared to the size of the training dataset.
But with DL, and for the moment this phenomena is not well understood, it seems that the larger the dataset, the better the generalization of the model, even if we increase the number of parameters of the model (broaden the function space).

\Rightarrow in short, as long the scaling is enough, there is a sensitive decoupling between the size of the dataset and the size of the model, and the risk of overfitting is mitigated (which is a big overcome of DL over classical ML in those datasets).

Quick bestiary

The Bestiary I, Dense Neural Networks

Very successful in tabular data (structured data), but also some standardised data (like MNIST). Used almost in every DL model as the last layers before output.

Dense Neural Networks (DNN): f_\theta(x) = \sigma(W_1 x + b_1) \circ \sigma(W_2 x + b_2) \circ \dots \circ \sigma(W_n x + b_n)
\sigma: activation function (ReLU, tanh, sigmoid, …)
W_i: weight matrix
b_i: bias vector
\theta = (W_1, b_1, \dots, W_n, b_n): parameters to learn

The Bestiary II, Convolutional Neural Networks

Immensely successful in computer vision.

Convolutional Neural Networks (CNN): f_\theta(x) = \sigma(W_1 \star x + b_1) \circ \sigma(W_2 \star x + b_2) \circ \dots \circ \sigma(W_n \star x + b_n)
\star: convolution operator
W_i: weight matrix
b_i: bias vector
\theta = (W_1, b_1, \dots, W_n, b_n): parameters to learn

The Bestiary IV, Recurrent Neural Networks

For sequences (first DL models for NLP and speech recognition).

The Bestiary V, Graph Neural Networks

Encodes graph structure (nodes, edges, global) into embedding vectors
Use those vectors as input to a network.
Attention mechanism \Rightarrow breakthrough of protein folding prediction with AlphaFold of DeepMind.

Jumper et al. (2021)

The Bestiary VI, Generative Adversarial Networks

GAN

[generative adversarial network for celebrity faces] (https://towardsdatascience.com/generative-adversarial-network-gan-for-dummies-a-step-by-step-tutorial-fdefff170391)

A quick history leading to ChatGPT

Grossing number of parameters and architectures
…

Tokens vs embeddings

(token: atomic unit) \neq (embedding: vector representation)

Tokenize the word: tokenizer
['token', '##izer']

pipeline to train a representation model (like BERT):
tokenize text \rightarrowmap token to a unique id \rightarrow map id to randomized initial vector \rightarrowtrain

BERT training set=books + wikipedia: Word completion + next sentence prediction