Week 1 Overview

For a 13 cm wing, the model predicts 5.5 m. The measured ground truth is 4.9 m.

A small model receives eight training examples. It studies two examples at a time.

After each pair, the model measures loss and adjusts its parameters once.

four updates

Backpropagation finds how each parameter affected the loss. An optimizer uses that information to choose a small update.

Suppose the training set has eight examples.

With batch size 2, two epochs contain eight updates: four updates in each epoch.

During recall practice, students answer from memory before checking the answer.

1. Population: the larger group that the study aims to understand.
2. Sample: the smaller group of students who take part.
3. Variables: the practice activity and the vocabulary score.

Researchers plan the question, sample, assignment, measurements, and analysis before collecting the data.

The scores stay in their rows. Advance to place the same two group labels into new rows.

Observed gap: 8 minus 4 equals 4. Shuffled gap: 5 minus 7 equals negative 2.

A p value asks how often the null model produces a result at least as unusual as the observed result.

Suppose a study estimates a 6 point average gain from recall practice.

The effect size, 6 points, describes the estimated difference. The confidence interval, 2 to 10 points, describes uncertainty under the procedure and assumptions.

Like two spotters, the hidden units identify A on and B off, or B on and A off. The output layer predicts open when either hidden unit is active.

The ReLU activation function keeps positive scores and replaces negative scores with zero. That step lets hidden units respond to different input regions.

Repeated iterations can produce hidden features such as the two XOR hidden units.

A test set stays reserved until the model choices are fixed. Its results describe that named set and scoring procedure.

The illustrative numerical claim is 5.5 m for a 13 cm wing.

In regression, software fits a line to measured pairs so that the fitted line can predict a number.

Mean squared error is a loss function that squares each residual and averages the squared values.

The middle equation has mean squared error 0, the smallest value in the table, so it fits these three averages best.

A sample is the set of flights measured by one class. Two classes can repeat the same designs and obtain different measurements.

Sampling variability is the change in an estimate across samples produced by the same measurement process.

The interval ranges from 0.35 to 0.65 m of predicted distance per additional centimetre of wing width.

A confidence interval procedure produces a new interval from each fresh sample.

If the assumptions hold, about 95 percent of intervals from many repeated samples would contain the fixed population slope.

The population slope is fixed. The interval endpoints change from sample to sample.

Under this null model, each measured distance can be paired with any fixed width without changing its probability. Statisticians call this exchangeability.

The alternative hypothesis states that width has a positive association with distance.

The observed assignment has slope +0.50.

One of the six equally likely assignments has a positive slope at least as large as the observed slope.

The calculation counts shuffled data patterns under the stated null model. A probability for the hypothesis requires a probability model for hypotheses and prior information.

The observed slope, 0.50 m per cm, reports the estimated magnitude. Future clearance requires a predictive model and evidence from new flights.

After a logistic classifier calculates a weighted score, z, it applies the sigmoid function, \sigma. The sigmoid function produces a value between 0 and 1.

The constant e is approximately 2.718. The resulting value is the probability that this model assigns to clearance.

If you answered about 70 cases, you were correct. Calibration compares predicted probabilities with observed frequencies among similar reserved cases.

With only ten cases, ordinary variation can move the observed count far from seven. Calibration needs many relevant cases.

A door opens when exactly one of two switches is on.

When the switches are plotted as two coordinates, the open cases occupy opposite corners. No single linear decision boundary separates both open cases from both closed cases.

Illustrative switch example. This pattern is called exclusive OR, commonly written XOR.

The ReLU function keeps positive numbers and replaces negative numbers with 0. Use the input with switch A on and switch B off.

Write off as 0 and on as 1. The ReLU function keeps positive values and replaces negative values with 0.

ReLU, pronounced ree loo, is the activation function \max(0,\text{score}). Negative scores become 0; positive scores remain unchanged.

The weights determine how strongly each input contributes. The bias shifts the score before the activation function is applied.

Place two switch examples in the rows of an input matrix, X. Place the weights for two hidden units in the columns of W.

The first row of X is the example (A,B)=(1,0). The second row is (1,1).

The first column of W calculates A-B. The second column calculates B-A.

Calculate each input row with both weight columns.

Apply ReLU to each entry, replacing the negative entry with 0.

Given the visible context, the model calculates one score for each possible next token.

Softmax uses the total, 6.66, as the denominator for every token.

During an ordinary chat response, the stored parameters remain fixed. A separate training process calculates gradients and updates those parameters.

Each row contains (i) wing width as the input and (ii) measured flight distance as the target.

Batch size is the number of examples used to calculate one update. Here, the batch size is 2.

A laundry load provides a capacity analogy: the dataset is the full pile, and one batch is the group processed together for one update.

Try the same batch with nearby settings of the weight.

The gradient gives the local slope of loss with respect to each parameter. Because this finite difference estimate is -2, a small increase in w decreases the loss near w=0.

Subtract the old squared loss from the new squared loss:

For flight A, \hat v-v=1 and \Delta\hat v=-0.1.

Illustrative continuation of the flight A calculation. As the size of a change approaches zero, its square approaches zero more quickly. For a tiny change, the term proportional to the change therefore gives a close approximation.

A partial derivative is a local slope with respect to one quantity while the other quantities remain fixed.

Backpropagation traverses the calculation in reverse and applies this chain rule at each step.

Use an illustrative learning rate of r=0.2. The estimated loss slope is g=-2.

The learning rate controls the step length along the gradient direction. Individual updates can vary, so training is assessed across many updates.

One iteration is one completed parameter update. One update contains (i) a forward pass, (ii) a loss calculation, (iii) a backward pass, and (iv) an optimizer step.

One iteration is one parameter update. One epoch is one complete pass through the training dataset.

Before another epoch, the program usually shuffles the examples and forms new batches. The updated parameters persist.

1. How many iterations occur in one epoch? 3 iterations.
2. How many updates occur across 3 epochs? 3(3)=9 updates.
3. How many examples are in the final batch? 10-4-4=2 examples.

In this illustrative example, suppose one scan enters training and software extracts a text copy for the test set. This extraction process is optical character recognition, or OCR.

Leakage occurs when information unavailable in the intended future use influences training or model selection.

A random row split can place related (i) rows, (ii) people, (iii) documents, or (iv) time periods in different partitions. Group related records before assigning partitions.

In this illustrative run, overfitting begins after epoch 3 because validation loss rises from 0.39 to 0.56 and training loss decreases during the same epochs.

1. Checkpoint storage: save parameter checkpoints during training.
2. Validation monitoring: measure validation loss.
3. Checkpoint selection: choose the checkpoint with the lowest validation loss.

After epoch 4 fails to improve on the saved validation loss, this illustrative procedure stops training and keeps the epoch 3 checkpoint. A separate test set provides the final estimate.

Before extracting text, record why the source is in scope.

1. Authority: who created or controls it?
2. Basis: (i) a license, (ii) permission, (iii) applicable terms, or (iv) another documented basis?
3. Purpose: does the intended training use match that basis?
4. Removal: how can corrections or exclusions propagate?

For this project, a public page enters review for (i) permission, (ii) privacy, (iii) attribution, and (iv) suitability before extraction.

After each transformation, the pipeline appends an entry to the provenance record.

1. Lineage: the input and output IDs connect the derivative to its source.
2. Responsibility: the operator and reviewer identify who performed and checked the work.
3. Reproducibility: the version identifies the transformation settings and source records in one release.
4. Separation: an automated validation check reads the partition field and rejects reserved records from training shards.

Exact deduplication compares identical normalized text or checksums. Deduplication for similar text uses fingerprints that tolerate small edits. D6 remains reserved for evaluation.

A mixture is a design decision, so chosen shares can differ from the raw collection. A shard is a manageable file portion used by the training system.

For next token training, the training program shifts each token sequence to construct its targets.

With self supervision, the training program constructs each target from sequence order.

This illustrative tokenizer treats each displayed word or number as one token. A deployed tokenizer may split text differently.

Cover one token in a complete sentence. Ask learners to predict it before revealing the recorded training target.

1. Sources created by people, including (i) lessons, (ii) books, (iii) code, (iv) discussions, and (v) archives, already embody human work.
2. Dataset teams perform (i) collection, (ii) rights review, (iii) OCR, (iv) filtering, (v) deduplication, (vi) mixing, and (vii) documentation.

Self supervision describes how the training program forms targets from sequence order. People (i) create, (ii) select, (iii) transform, (iv) document, and (v) govern the dataset.

Supervised fine tuning, or SFT, updates the model toward approved responses to recorded prompts.

In this illustrative reward model, one learnable parameter, q, equals the difference between the two candidate scores. A full reward model calculates both scores from many weights.

The sigmoid function converts the score difference into a 57 percent predicted preference for A. The recorded judgment says that A was chosen.

The correction supplies the direction for updating the illustrative parameter q.

This illustrative reward model has one parameter, q_{\text{old}}=0.3. Use an illustrative learning rate of 0.2 for the update.

After the optimizer updates q, another forward calculation gives a predicted preference of about 60 percent for A.

Training software uses repeated comparisons across many batches and optimizer updates to train a reward model. A full reward model updates the weights that produce both candidate scores.

Reinforcement learning from human feedback, or RLHF, uses the trained reward model to score new responses.

Proximal policy optimization, or PPO, uses those scores to update the language model. In InstructGPT, a probability penalty at each token discourages the updated language model from assigning token probabilities that differ greatly from the SFT reference model.

The checks for (i) exact text, (ii) similar text, and (iii) shared source groups answer different contamination questions. The record stores (i) the method, (ii) the threshold, (iii) the result, and (iv) the review status.

Illustrative checks. Contamination checks compare evaluation records with the indexes for every training release.

Report (i) the numerator, (ii) the denominator, (iii) the dataset version, (iv) the scoring rule, and (v) results by relevant topic or group.

For this illustrative calculation, define the population as grade 9 science questions that satisfy evaluation specification 1.0.

Additional evaluation sets are needed for (i) other tasks, (ii) other populations, and (iii) other deployment conditions.

1. Which records form one duplicate group? The duplicate group contains (i) D1, (ii) D4, and (iii) D5.
2. When should the group be assigned to a split? Assign the duplicate group to one partition before creating chunks.
3. May D6 become a synthetic SFT prompt? D6 remains a reserved evaluation record and stays outside synthetic SFT generation.
4. Do 52 preference wins out of 100 establish a dependable lead? A lead of four cases requires an interval or repeated evidence before it supports a strong claim.

An image encoder is the part of a vision model that represents an image with numerical features. Here, it multiplies the patch vector by a learned weight matrix.

The four rows match the four pixel values. The two columns produce two output values. This matrix is illustrative.

The result, a vector with two values, is a patch embedding. Practical image encoders commonly calculate patch embeddings from larger patches and use a larger embedding dimension, which is the number of columns in W. The optimizer updates the entries of W during training.

Illustrative patch embedding calculation.

1. Prediction and label: the regression line produced the 5.5 m prediction, and the decision threshold assigned the label clears.
2. Uncertainty: repeated samples and a stated statistical model support a confidence interval.
3. Generated explanation: at each generation step, the network calculated token scores from learned features, and the softmax function converted those scores into probabilities.
4. Learned parameters: the training program (i) ran forward passes, (ii) calculated losses, (iii) ran backward passes, and (iv) applied optimizer updates across batches and epochs.
5. Evidence base: records document (i) source provenance, (ii) OCR review, (iii) pretraining, (iv) SFT, (v) preference annotation, and (vi) reserved evaluation. They show how people (i) prepared the data, (ii) trained the model, and (iii) evaluated the fixed model.