_index.org

Newton's First Law of Motion

Last edited: August 8, 2025

\begin{equation} y’’=0 \end{equation}

that is, if \(F=0\), then the solution will travel along a straight line.

Newton's Law of Cooling

Last edited: August 8, 2025

Putting something with a different temperature in a space with a constant temperature. The assumption underlying here is that the overall room temperature stays constant (i.e. the thing that’s cooling is so small that it doesn’t hurt room temperature).

\begin{equation} y’(t) = -k(y-T_0) \end{equation}

where, \(T_0\) is the initial temperature.

The intuition of this modeling is that there is some \(T_0\), which as the temperature \(y\) of your object gets closer to t. The result we obtain

NL

Last edited: August 8, 2025

\begin{equation} \text{NL} = \text{NSPACE} \qty( \log n) \end{equation}

See also Certificates-Based Intepretation of NL

problems in \(NL\)

We can see \(L \subseteq NL\), because a TM is a NTM.

STCONN is in NL

On input \(\qty(G, s,t)\), if \(s = t\), accept; otherwise,

  • currNode = 5
  • numSteps = 0
  • while steps <= n
    • non-deterministically choose a next node
    • update currNode = w
    • if w = t, accept
    • set numSteps ++
  • reject

so we just have to remember the current node. So this whole thing is \(O\qty(\log n)\).

NLP

Last edited: August 8, 2025

Complex System

Coherence

Generative REVOLUTION

Why probability maximization sucks

Its expensive!

  1. Take \(k\) candidates
  2. Expand \(k\) expansions for each of the \(k\) candidates
  3. Choose the highest probability \(k\) candidates

\(k\) should be small: trying to maximizing

Branch and Bound

See Branch and Bound

Challenges of Direct Sampling

Direct Sampling sucks. Its sucks. It sucks. Just sampling from the distribution sucks. This has to do with the fact that assigning slightly lower scores “being less confident” is exponentially worse.

NLP Index

Last edited: August 8, 2025

Learning Goals

  1. Effective modern methods for deep NLP
    • Word vectors, FFNN, recurrent networks, attention
    • Transformers, encoder/decoder, pre-training, post-training (RLHF, SFT), adaptation, interoperability, agents
  2. Big picture in HUMAN LANGUAGES
    • why are they hard
    • why using computers to deal with them are doubly hard
  3. Making stuff (in PyTorch)
    • word meaning
    • dependency parsing
    • machine translation
    • QA

Lectures