12 - Terra Incognita

Question 1

What is the addition operation described in the context of binary numbers?

Answer 1

Addition is performed modulo-97, meaning sums wrap around between 0 and 96.

Question 2

How is the sum expressed in modulo-97 addition?

Answer 2

sum = x + (some multiple of 97), where 0 ≤ x ≤ 96.

Question 3

What does ‘grokking’ refer to in the context of neural networks?

Answer 3

‘Grokking’ is a term used to describe a deep understanding and internalization of information by a neural network.

Question 4

What is the relationship between the number of parameters in a neural network and its performance?

Answer 4

More parameters can lead to overfitting, while fewer parameters can lead to underfitting.

Question 5

What is overfitting in machine learning?

Answer 5

Overfitting occurs when a model learns details and noise in the training data to the extent that it negatively impacts its performance on new data.

Question 6

What is underfitting in machine learning?

Answer 6

Underfitting occurs when a model is too simple to capture the underlying pattern of the data.

Question 7

Describe the bias-variance trade-off.

Answer 7

High bias leads to underfitting, while high variance leads to overfitting. The goal is to find a balance between the two.

Question 8

What is the role of the test dataset in machine learning?

Answer 8

The test dataset is used to evaluate the model’s performance on unseen data, indicating its ability to generalize.

Question 9

What happens when a model is too complex?

Answer 9

It may overfit the training data, leading to poor performance on test data due to capturing noise.

Question 10

What is a simple model’s performance on noisy data?

Answer 10

A simple model may ignore noise, leading to high training and test errors.

Question 11

Fill in the blank: The number of ________ in a model determines its complexity and capacity.

Answer 11

[parameters]

Question 12

True or False: A model with too few parameters will have a high risk of overfitting.

Answer 12

False

Question 13

What is the consequence of a model that tracks every variation in the training data?

Answer 13

It leads to overfitting and poor generalization to test data.

Question 14

What does the capacity of a hypothesis class refer to?

Answer 14

It refers to the range of functions that a model can approximate based on its parameters.

Question 15

What is the universal approximation theorem?

Answer 15

It states that a neural network with sufficient neurons can approximate any function.

Question 16

How does model complexity affect training risk?

Answer 16

Training risk decreases as model complexity increases, up to a point, after which it may increase due to overfitting.

Question 17

What is the consequence of using a very simple model on complex data?

Answer 17

It will likely result in high training and test errors due to underfitting.

Question 18

Fill in the blank: The goal of an ML engineer is to find the sweet spot between ________ and variance.

Answer 18

[bias]

Question 19

What is one of the most significant challenges in model selection?

Answer 19

Determining the right level of complexity to avoid underfitting and overfitting.

Question 20

What happens to test error when a model is too complex?

Answer 20

The test error tends to increase due to overfitting.

Question 21

Describe the performance of a model that has a high bias.

Answer 21

It will likely underfit the training data and perform poorly on test data.

Question 22

What does a highly complex, nonlinear model do during training?

Answer 22

It minimizes training errors but may generalize poorly to test data.

Question 23

What happens to the capacity of the hypothesis class when the number of parameters is increased?

Answer 23

It increases the capacity of the hypothesis class.

Question 24

What does the dashed curve in the figure represent?

Answer 24

The training risk, or the risk that the model makes errors on the training dataset.

Question 25

What is the effect of extremely simple models on training data?

Answer 25

They do badly because they are underfitting the data.

Question 26

What happens to the training risk as model complexity increases?

Answer 26

It goes to zero as models start overfitting.

Question 27

What does the solid curve in the figure represent?

Answer 27

The risk of error during testing.

Question 28

What is the 'Goldilocks zone' in model selection?

Answer 28

The optimal balance between underfitting and overfitting.

Question 29

What is the relationship between minimizing test error and generalization ability?

Answer 29

Minimizing test error implies minimizing generalization error.

Question 30

What is the conventional wisdom regarding deep neural networks and their parameters?

Answer 30

They are over-parameterized and should not generalize well.

Question 31

What surprising observation did Neyshabur and colleagues make about deep neural networks?

Answer 31

Increasing the size of the network did not cause it to overfit the training data.

Question 32

What phenomenon occurs when noise is introduced into the dataset?

Answer 32

The model accommodates the noise and may still achieve zero training error.

Question 33

What does it mean when a model is said to 'shatter' the training data?

Answer 33

It fits the training data perfectly, including any noise.

Question 34

What did Neyshabur and colleagues find regarding test error with noisy data?

Answer 34

Test error continued decreasing as network size increased past the size required for zero training error.

Question 35

What potential explanation did Neyshabur and colleagues suggest for this behavior?

Answer 35

Implicit regularization by stochastic gradient descent.

Question 36

What did Chiyuan Zhang and colleagues conclude about neural networks in their 2016 paper?

Answer 36

The effective capacity of several successful neural network architectures is large enough to shatter the training data.

Question 37

What is 'benign overfitting'?

Answer 37

The phenomenon where models can fit noisy data without significant overfitting.

Question 38

What is the role of hyperparameters in neural network training?

Answer 38

They are set by engineers before training begins and influence model architecture and training process.

Question 39

What are feedforward neural networks?

Answer 39

Networks where information flows one way from input to output.

Question 40

What are recurrent neural networks known for?

Answer 40

Allowing feedback connections to remember previous inputs.

Question 41

What is the backpropagation algorithm used for?

Answer 41

Training neural networks by minimizing loss.

Question 42

What is a loss function in the context of neural networks?

Answer 42

A function that calculates the error made by the network.

Question 43

What is the purpose of regularization in neural networks?

Answer 43

To prevent overfitting by controlling model complexity.

Question 44

What is one method of explicit regularization?

Answer 44

Preventing the values for the weights from getting too large.

Question 45

What is a unique method used to prevent overfitting during training?

Answer 45

Randomly dropping some connections in the network.

Question 46

What must activation functions be for backpropagation to work?

Answer 46

Differentiable.

Question 47

What is a method to prevent overfitting in neural networks?

Answer 47

Randomly drop some connections during training ## Footnote This technique reduces the number of effective parameters.

Question 48

What is required for an activation function to work with backpropagation?

Answer 48

The activation functions must be differentiable ## Footnote Some functions, like ReLU, are not differentiable at specific points but can still be used.

Question 49

What is the primary difference between supervised learning and unsupervised learning?

Answer 49

Supervised learning requires labeled training data, while unsupervised learning does not ## Footnote In unsupervised learning, the algorithm identifies clusters without explicit labels.

Question 50

What is self-supervised learning?

Answer 50

A method that creates implicit labels from unlabeled data without human involvement ## Footnote This approach has led to significant advancements in AI, such as ChatGPT.

Question 51

Who developed a deep neural network solution for pattern analysis at UC Berkeley in 2014?

Answer 51

Jitendra Malik and colleagues ## Footnote Their work focused on the PASCAL VOC dataset.

Question 52

What does R-CNN stand for?

Answer 52

Region-based Convolutional Neural Network ## Footnote R-CNN outperformed existing methods in object detection after being fine-tuned.

Question 53

What was the initial concern of Alexei Efros about R-CNN?

Answer 53

Why a network trained on ImageNet could detect object boundaries well after fine-tuning ## Footnote Efros believed the CNN needed general information from ImageNet for effective boundary detection.

Question 54

What was the outcome of the bet between Efros and Malik?

Answer 54

Efros lost the bet when R-CNN remained the best for object detection ## Footnote The bet was about achieving object detection without human annotations.

Question 55

How do large language models (LLMs) like GPT-3 learn?

Answer 55

They predict masked words in sentences from a large corpus of text ## Footnote The learning process involves calculating loss and updating parameters.

Question 56

What is the goal of the masked auto-encoder (MAE) developed by Kaiming He and colleagues?

Answer 56

To generate unmasked images from masked input images ## Footnote The MAE learns latent representations of key features in images.

Question 57

What is double descent in machine learning?

Answer 57

A phenomenon where increasing model capacity leads to improved performance beyond interpolation ## Footnote It includes a first descent to a minimum test error, followed by an ascent, and a second descent.

Question 58

What does the term 'terra incognita' refer to in the context of deep learning?

Answer 58

The unexplored mathematical underpinnings of observed behaviors in over-parameterized neural networks ## Footnote This contrasts with the well-understood behavior in under-parameterized regimes.

Question 59

What tension exists in the machine learning community according to Tom Goldstein?

Answer 59

The tension between theoretical and experimental approaches in machine learning ## Footnote This has implications for the development of new models and understanding their behavior.

Question 60

What is a significant challenge when dealing with the loss function of deep neural networks?

Answer 60

The loss function is non-convex with many local minima ## Footnote This complicates the process of finding the global minimum.

Question 61

True or False: The loss landscape of deep neural networks is well understood.

Answer 61

False ## Footnote There are conflicting theories about the existence of local minima in the loss landscape.

Question 62

What is the nature of the loss landscape in deep neural networks?

Answer 62

It is extremely complicated and may contain local minima or global minima ## Footnote The landscape's complexity is a significant challenge for theorists.

Question 63

What did Goldstein's empirical study reveal about local minima in neural networks?

Answer 63

Neural networks can get stuck in not-so-good local minima where the loss is non-zero ## Footnote This occurs despite the networks being over-parameterized.

Question 64

What is stochastic gradient descent?

Answer 64

A method where gradient descent is performed using small batches of training data ## Footnote It approximates the descent direction rather than using the exact steepest descent.

Question 65

What does the term 'grokking' refer to in the context of neural networks?

Answer 65

The phenomenon where a neural network learns to generalize beyond mere memorization after extensive training ## Footnote It involves understanding deeper patterns in the data.

Question 66

What is a transformer in machine learning?

Answer 66

A type of architecture especially suited for processing sequential data ## Footnote Examples include LLMs like ChatGPT.

Question 67

How did the transformer network used by Power's team learn to add numbers?

Answer 67

It was trained on a table of modulo-97 addition examples and learned to represent numbers in a high-dimensional space ## Footnote The learning process involved predicting masked numbers in the addition equations.

Question 68

What happens when a transformer network stops training after reaching zero training loss?

Answer 68

It likely interpolates the training data and memorizes it ## Footnote This results in poor performance on unseen test data.

Question 69

What is a phase change in the context of grokking?

Answer 69

The transition from memorizing a table of answers to understanding underlying knowledge ## Footnote It is likened to physical phase changes, such as water turning to ice.

Question 70

What is the significance of Minerva in language models?

Answer 70

It was the first LLM to correctly answer about 50% of high school-level math questions in the MATH dataset ## Footnote Minerva used a large language model architecture to predict answers based on token sequences.

Question 71

How does Minerva generate answers to math questions?

Answer 71

It converts the question into a sequence of tokens and predicts the answer token by token ## Footnote This raises questions about whether it is reasoning or merely pattern matching.

Question 72

What are AI winters?

Answer 72

Periods of stagnation in AI research due to lack of progress or overhyped expectations ## Footnote Notable AI winters occurred in the late 1960s, 1970s, and late 1980s.

Question 73

What does Goldstein argue about the current state of AI research?

Answer 73

We may still be experiencing an AI winter regarding tasks that involve text comprehension and logical reasoning ## Footnote There's ongoing debate about the effectiveness of neural networks alone in achieving true AI.

Question 74

What was the training approach used for both PaLM and Minerva?

Answer 74

They were trained using self-supervised learning to predict masked tokens ## Footnote This method does not involve explicit reasoning or problem-solving.

Question 75

Fill in the blank: The addition operation in the training data used by Power's team was _______.

Answer 75

modulo-97 addition