One-Liner

Novelty

Notable Methods

Key Figs

New Concepts

Notes

One-Liner

Notable Methods

1. construct a series of perturbation actions
   • \(A\qty(s)\) = decomposition (skip), expansion (rollout), dredirection
2. sequence actions with MCTS

Key Figs

New Concepts

Notes

Motivation: drug discovery is extremely slow and expensive; mostly modulating previous iterations of work.

Principles of Drug Discovery

• observation: acquire/fuse knowledge from multiple data modalities (sequence, stricture, etc.)
• think: critically generating actually new hypothesis — allowing iteratively
• allowing LMs to code-switch between moladities (i.e. fuse different modalities together in the most uniform way)

LM as a heuristic helps prune down search space quickly.

• matrix calculus
• supervised learning
• gradient descent
• Newton’s Method
• regression
  • \(y|x,\theta\) is linear Linear Regression
    • least-squares error: probabilistic intuition for least-squares error in linear regression
    • Normal Equation
  • What if \(X\) and \(y\) are not linearly related? Generalized Linear Model
    • \(y|x, \theta\) can be any distribution that’s exponential family
    • some exponential family distributinos: SU-CS229 Distribution Sheet
• classification
  • take linear regression, squish it: logistic regression; for multi-class, use softmax \(p\qty(y=k|x) = \frac{\exp \theta_{k}^{T} x}{\sum_{j}^{} \exp \theta_{j}^{T} x}\)
  • generative learning
    • modeling each class’ distributions, and then check which one is more likely: GDA
    • Naive Bayes
• bias variance tradeoff
• regularization
• unsupervised learning
  • k-means clustering
  • Gaussian mixture model and expectation maximization
    • Jensen’s Inequality
• feature map and precomputing Kernel Trick
• Decision Tree
• boosting

backpropegation is a special case of “backwards differentiation” to update a computation grap.h

constituents

• chain rule: suppose \(J=J\qty(g_{1}…g_{k}), g_{i} = g_{i}\qty(\theta_{1} \dots \theta_{p})\), then \(\pdv{J}{\theta_{i}} = \sum_{j=1}^{K} \pdv{J}{g_{j}} \pdv{g_{j}}{\theta_{i}}\)
• a neural network

requirements

Consider the notation in the following two layer NN:

\begin{equation} z = w^{(1)} x + b^{(1)} \end{equation}

\begin{equation} a = \text{ReLU}\qty(z) \end{equation}

\begin{equation} h_{\theta}\qty(x) = w^{(2)} a + b^{(2)} \end{equation}

\begin{equation} J = \frac{1}{2}\qty(y - h_{\theta}\qty(x))^{2} \end{equation}

1. in a forward pass, compute the values of each value \(z^{(1)}, a^{(1)}, \ldots\)
2. in a backward pass, compute…
   1. \(\pdv{J}{z^{(f)}}\): by hand
   2. \(\pdv{J}{a^{(f-1)}}\): lemma 3 below
   3. \(\pdv{J}{z^{f-1}}\): lemma 2 below
   4. \(\pdv{J}{a^{(f-2)}}\): lemma 3 below
   5. \(\pdv{J}{z^{f-2}}\): lemme 2 below
   6. and so on… until we get to the first layer
3. after obtaining all of these, we compute the weight matrices'
   1. \(\pdv{J}{W^{(f)}}\): lemma 1 below
   2. \(\pdv{J}{W^{(f-1)}}\): lemma 1 below
   3. …, until we get tot he first layer

chain rule lemmas

Pattern match your expressions against these, from the last layer to the first layer, to amortize computation.