Lab

A game and six toys for getting your hands on the mechanisms. They all run in your browser on toy data: they don’t replace real models, but they let you see the idea without intermediaries. At the end, a notebook for trying a real model.

Who’s that model?

See: Base stats (how to read an entry)

Keys 1–4 or arrows

Attention: who looks at whom

See: Self-attention · Causal mask · Encoder · Decoder · Transformer · BERT · GPT-2

Bidirectional (encoder, like BERT) Causal (decoder, like GPT)

Pick a word: the lines show which other words it “attends” to, and how strongly.

Attention matrix (rows: who asks; columns: whom)

Weights set by hand for illustration, not taken from a real model. Look at “it”: it attends mostly to “animal”, the phrase it refers to. In causal mode every word can only look back, so “animal” cannot consult “tired”.

Temperature and sampling

See: Softmax · Logits · Temperature · Sampling (top-k, top-p) · GPT-3 · ChatGPT (InstructGPT)

The cat jumped onto the…

Temperature 1.0Top-p (nucleus) 1.00

The logits are made up. At low temperature the distribution piles onto the most likely option (almost greedy decoding); at high temperature it flattens and odd continuations appear. Top-p cuts the tail: sampling only among the most likely options that add up to p.

Byte-pair encoding (BPE)

See: Token · Tokenization · Byte-pair encoding (BPE) · Vocabulary · GPT-2

Type or paste a text. The BPE algorithm starts from single characters and, at each step, merges the most frequent neighboring pair. Move the slider to watch subwords appear.

Merges 0

Learned merges, in order

A real tokenizer learns tens of thousands of merges over a huge corpus; this one learns only from your text. The ▁ symbol marks the start of a word. Notice that merges follow frequency, not morphology: sometimes they match morphemes (play-, -ed, -s) and sometimes they don’t.

Vector spaces and analogies

See: Embedding · Cosine similarity · Distributional hypothesis · Vector · word2vec

A − B + C

Coordinates placed by hand in two dimensions so the idea is visible. Real embeddings have hundreds of dimensions, are learned from how words are distributed in a corpus, and analogies work considerably worse than this textbook example suggests (part of their apparent success depends on excluding the input words).

The perceptron learns (or not)

See: Decision boundary · Gradient descent · Nonlinearity · Perceptron · Multilayer perceptron (backprop)

Click to add points of the selected class. The perceptron fixes its weights every time it misclassifies a point: w ← w + η·(y − ŷ)·x.

With the keyboard: arrows move the crosshair, Enter adds a point.

Class A Class B

With linearly separable data, the perceptron converges (Rosenblatt’s convergence theorem). With XOR no straight line separates the classes: the line wobbles forever. That limitation, stressed by Minsky and Papert in 1969, is only overcome with hidden layers.

A decision tree for the weather

See: Entropy and information gain · Classification · Overfitting · Decision tree (ID3/C4.5)

Information gain of each attribute at the root

Tree root:

Resulting tree

The 14 days of the “weather” dataset

The “weather” dataset is fictitious and tiny; Witten et al. use it throughout their book, taken from Quinlan (1986). Choosing the root by information gain gives the tree of their Figure 4.4. Try forcing a different root: the tree grows and becomes harder to read, even though it fits the training data just as well. (Witten et al., 2017, pp. 10, 106–109)

Notebooks

See: Natural language inference (NLI) · Fine-tuning · Bi-encoders and cross-encoders · Classification · BERT

Google Colab notebooks that load real models. They run on Google’s servers, not in your browser.

BERT and natural language inference

A REFERENTIA notebook that loads a classifier already fine-tuned on MultiNLI and asks it to judge premise–hypothesis pairs as entailment, contradiction or neutral (natural language inference). The model is roberta-large-mnli, that is, RoBERTa, one of BERT’s regional forms (Y. Liu et al., 2019). It works as a cross-encoder: it reads premise and hypothesis together, joined by special tokens, and returns one of the three labels with its probability.

It runs on Google Colab and needs a Google account: save a copy to your Drive and run the cells in order. The explanations are in Spanish; write the sentences in English, since the model was trained on MNLI.

Pairs to try

Premise The doctor was paid by the actor.
Hypothesis The doctor paid the actor.
Same words, different order: the right answer is not entailment. Models trained on MNLI tend to say it is (McCoy et al., 2019, p. 3429).
Premise No dog is running in the park.
Hypothesis No puppy is running in the park.
Entailment: “no” reverses the direction, and what holds of all dogs holds of puppies. Then change No to Some in both sentences: it no longer follows. Downward-entailing contexts are harder for models (Yanaka et al., 2019).
Premise A boat sank in the Pacific Ocean.
Hypothesis A boat sank in the Atlantic Ocean.
Contradiction or neutral? It depends on whether they describe the same boat, a convention the SNLI authors had to fix for their annotators (Bowman et al., 2015, p. 633).

Open in Colab