➩ \(a^{\left(h\right)}_{t} = g\left(w^{\left(x\right)} \cdot x_{t} + b^{\left(x\right)}\right)\) is not recurrent.

➩ There are value units \(a^{\left(v\right)}_{t} = w^{\left(v\right)} \cdot a^{\left(h\right)}_{t}\), key units \(a^{\left(k\right)}_{t} = w^{\left(k\right)} \cdot a^{\left(h\right)}_{t}\), and query units \(a^{\left(q\right)}_{t} = w^{\left(q\right)} \cdot a^{\left(h\right)}_{t}\), and attention context can be computed as \(g\left(\dfrac{a^{\left(q\right)}_{s} \cdot a^{\left(k\right)}_{t}}{\sqrt{m}}\right) \cdot a^{\left(v\right)}_{t}\) where \(g\) is the softmax activation: here \(a^{\left(q\right)}_{s}\) represents the first word, \(a^{\left(k\right)}_{t}\) represents the second word, \(a^{\left(q\right)}_{s} \cdot a^{\left(k\right)}_{t}\) is the dot product (which represents the cosine of the angle between the two words, i.e. how similar or related the two words are), and \(a^{\left(v\right)}_{t}\) is the value of the second word to send to the next layer.

➩ The attention matrix is usually masked so that a unit \(a_{t}\) cannot pay attention to another unit in the future \(a_{t+1}, a_{t+2}, a_{t+3}, ...\) by making the \(a^{\left(q\right)}_{s} \cdot a^{\left(k\right)}_{t} = -\infty\) when \(s \geq t\) so that \(e^{a^{\left(q\right)}_{s} \cdot a^{\left(k\right)}_{t}} = 0\) when \(s \geq t\).

➩ There can be multiple parallel attention units called multi-head attention.

➩ Attention mechanism (multi-head attention).

➩ Feed-forward network.

➩ Residual connections.

➩ Word2vec: Wikipedia.

➩ Universal sentence encoder: Link.

➩ Trained weights, or,

➩ Calculated by \(P\left(k, 2 i\right) = \sin\left(\dfrac{k}{n^{2 i / d}}\right)\) and \(P\left(k, 2 i + 1\right) = \cos\left(\dfrac{k}{n^{2 i / d}}\right)\) for word token \(k\) to position \(j \in \left\{2 i, 2 i + 1\right\}\) in the embedding vector: Link.

➩ Attention mechanism produces contextual embeddings.

➩ Input \(a_{i}\), compute \(\mu_{x} = \dfrac{1}{d} \displaystyle\sum_{i=1}^{d} x_{i}\) and \(\sigma^{2}_{x} = \dfrac{1}{d} \displaystyle\sum_{i=1}^{d} \left(x_{i} - \mu_{x}\right)^{2}\).

➩ Output \(a^{\left(n\right)}_{i} = \dfrac{a_{i} - \mu_{x}}{\sqrt{\sigma^{2}_{x} + \varepsilon}}\), added \(\varepsilon\) small to prevent \(\sigma\) close to 0.

➩ Encoder: input sequence to a continuous representation \(z\) (useful for classification).

➩ Decoder: from \(z\), generate output sequence (useful for generation).

➩ Pre-training: train all the weights on general purpose text dataset to learn contextualized word and sentence representations.

➩ Fine tuning for pre-trained decoder models freezes a subset of the weights (usually in earlier layers) and updates the other weights (usually the later layers) based on new datasets: Wikipedia.

➩ Fine tuning for pre-training encoder models adds task heads (additional layers at the end) and trains the weights in the task heads (sometimes also updates the pre-trained weights) for specific tasks.

➩ Prompt engineering does not alter the weights, and only provides more context (in the form of examples): Link, Wikipedia.

➩ Reinforcement learning from human feedback (RLHF) uses reinforcement learning techniques to update the model based on human feedback (in the form of rewards, and the model optimizes the reward instead of some form of costs): Wikipedia.

➩ Social networks: individuals related by friendship.

➩ Biology and chemistry: bonds between compounds or molecules.

➩ Citation networks: scientific paper cite each other.

➩ Features: title, abstract, authors.

➩ Labels: math, science, engineering.

➩ More signal from the relationships: cite each other, more likely from the same field.

➩ Images can be viewed as graphs where pixels are nodes and neighboring pixels are connected by edges.

➩ An example of \(A_{G} = D^{- \dfrac{1}{2}} A D^{- \dfrac{1}{2}}\).

➩ Local: downsampling, for example, k-nearest neighbor pooling, top-k pooling.

➩ Global: permutation invariant, for example, sum, mean, maximum.

➩ CNN share weights over space (regions of pixels).

➩ RNN share weights over time (sequences of tokens).

➩ GNN share weights over graph neighborhoods (links or edges in the graph).

➩ Submit relevant answers to the questions discussed during the lecture: incorrect answers are okay.

➩ Some questions require [notes] to earn the point.

➩ Some questions require special ID (given during the lecture) to earn the point.

➩ Do not submit answers to questions that are not discussed during the lectures. Each such submission will result in a deduction of one point.

➩ The grade on Canvas Assignment W12 is computed as number of points divided by the number of questions asked (and multiplied by 4, out of 4) and updated on Canvas every weekend.