Category: Concepts

Projects I’m contemplating

  • Concept: Rational Reader

    This is a sketch of a solution to Task: text to Bayes rationality.

    The paradigm is Bayesian epistemology. The broader task is to infer a rational worldview from empirical observation. Here, we use a collection of documents as our link to the real world: we observe that somebody created a document like this.

    Roughly speaking, we infer our rational worldview by forcing Bayes’ rule in all possible combinations of model weights and observations. The engine of this arrangement is a language model conditioned on propositional knowledge paired with a knowledge model conditioned on language.

    Preliminaries

    In reality, there are at least two Bayes’ rules: the discrete and the continuous. We we use the continuous form:

    $$f_{X|Y=y}(x) = f_{Y|X=x}(y) f_{X}(x) / f_{Y}(y)$$

    where each function is a probability density function / conditional density.

    To make a continuous distribution over something discrete like words, we use a traditional word embedding summed with positional encoding, then passed through the PDF of a multivariate normal distribution with inferred mean and covariance matrix. (How this interacts with the positional encoding I’m not clear on….)

    The multivariate normal is particularly useful because it can be arbitrarily marginalized to any subset of components of the random vector; this results from the fact that a multivariate normal parameterized by a linear transform of another’s parameters is also multivariate normal.

    Distributions of interest

    There are five:

    • $P(\vec{w})$—a general language model. This decomposes by the chain rule as $P(\vec{w}) = \Pi_{i} P(w_i | \vec{w}_{j < i})$.

      Implementation: unclear; we need a probabilistic language model; can we get a probabilistic interpretation of a transformer?
    • $P(K)$—a general knowledge model. How likely, a priori, is a belief or statement to be true?

      Implementation: a multivariate normal would be a starting point
    • $P(\vec{w} | K)$—the knowledge-conditional language model. This is the probability of a document $\vec{w}$ given some assertion of the state of the world, the nature of reality, or whatever, $K$. $K$ may make claims about a subset of reality; the world is a complex place, so it’s helpful to be able to discuss parts of it rather than always the whole. This is enabled by the marginalizability of the multivariate normal as discussed above. Of course by the chain rule this decomposes to $\Pi_{i} P(w_i | \vec{w}_{j < i})$.

      Implementation: uncertain; a multivariate normal parameterized by a transformer with $K$ as input?
    • $P(K | \vec{w})$—the language-conditional knowledge model. Given a word and its context, how likely is an assertion about our model to be true?

      Implementation: uncertain; another probabilistic transformer? A multivariate normal whose parameters are a function of $\vec{w}$, perhaps the output of a transformer?
    • $P(K|J)$ where $K$ and $J$ are disjoint propositions—a hypotheticals model. What does assuming part of our model say about the rest of our model?

      Implementation: multivariate normal parameterized by output of a transformer

    Training Procedure

    Randomly sample word-with-context $\vec{w}$ and knowledge vector $\vec{k}$. Randomly partition $\vec{k}$ into disjoint vectors $\vec{q}$ and $\vec{r}$. Compute the gradient of the loss:

    $$\mathfrak{L}_{Int} = [P(\vec{q} | \vec{r}) – P(\vec{r} | \vec{q}) P(\vec{q}) / P(\vec{r})]^2$$

    $$\mathfrak{L}_{Obs} = [P(\vec{w} | \vec{k}) – P(\vec{k} | \vec{w}) P(\vec{w}) / P(\vec{k})]^2$$

    $$\mathfrak{L} = \mathfrak{L}_{Int} + \mathfrak{L}_{Obs}$$

    and feed it to your favorite optimizer.

    The first part critically evaluates the interrelationship of model components. The second part critically evaluates the explanatory power of the model relative to empirical observation.

  • Concept: Maximum Basic Goodness

    (Updated by Concept: Maximum Basic Goodness 2)

    A blockchain-based system for voluntary wealth redistribution.

    Components:

    • Attestation of humanity: authorities that cryptographically attest that a given person is (within their system) a unique human being, not otherwise represented.
    • Ability to publicly or anonymous donate to all people that meet a particular proof of humanness, e.g. every human attested by a state’s vital records division
    • Ability to publicly (or anonymously?) subscribe to receive donations
    • Ability to pledge certain amount and frequency of donations in the future
  • Concept: Artificial language generator

    Using Generative Adversarial Networks combined with neural machine translation (NMT) generate believable English->Foreign translation models for de novo non-existent languages. How can Tolkien’s creation of Elvish be reproduced automatically for novel language instances?

    See also Concept: Phonotactics embedding

  • Concept: Rehearsal app, suggested by Joe Haws

    A cross-platform mobile app that allows adding an audio track and setting rehearsal marks (A, B, C, etc) and then tapping a button to trigger playback from a particular mark.

    React Native?

  • Concept: “Dinner” app—meet new people by feeding them dinner

    Ad-hoc dinner groups. Ratings let you distinguish leeches.

  • Concept: Improved Reference System 1

    World Wide Web current failings:

    • No recognized way of referencing passages of documents
    • Fragment identifiers cannot be used to efficiently reference down to the word or character level.
    • Linked documents have a tendency to disappear, thus rendering references less useful
    • No recognized way of referring to a particular version of a document, whose integrity is guaranteed

    Solution:

    • Introduce sub-fragment references syntax for href:
      <a href=”http://example.com/document#fragment[495,w24,513-859,1021,1249-1250]”>
    • List of character/character range references
    • This depends on a knowing the document’s character set
    • List of word/word range references
    • This depends on a tokenization algorithm
    • Introduce document content hash syntax for href:
      <a href=”http://example.com/document@a9e1bb2429″>…</a>
      <a href=”object://a9e1bb2429″>…</a>
    • Extend HTTP to allow request of specific document versions ?
      This is actually probably handled fine at the application layer
    • Define standard for embedding referenced documents into an HTML document, e.g.
    <html>
    <head>
     <object hash="a9e1bb2429">
      <!DOCTYPE html>
      <html>
      ...
      </html>
     </object>
     <object hash="ff4d042c90">
     ...
     </object>
    </head>
    <body>...</body>
    </html>

    <object> is like an <iframe>

    The hash attribute has no effect? Just there to help developers? But it violates DRY because it can be computed.

  • Concept: Language Thing

    • Second language learning assistant by means of machine translation
    • See $HOME/Projects/Glossy
    • Uploading/archiving/tagging of speech samples — a dialect/pronunciation database
    • See $HOME/HowITalk
    • Word frequency map (geographical map) based on twitter data
    • See $HOME/Projects/WordFreqMining

  • Concept: Reccomenu

    User rates dishes purchased at restaurants. Make recommendations for other dishes (as function of adventuresomeness) using collaborative filtering with other users’ ratings.

    Strong emphasis on privacy / minimizing data collection. Simplicity.

    Users could be rated by how daring they are, clustered by their typical tastes, etc.

  • Concept: Calendar database / exchange

    • Allow uploading and searching of calendars, such as could be subscribed to in Google Calendar, etc.
      • Use case: subscribe to BYU events calendar instead of having to load a web page to view it
    • Automatic inference of calendar events from event websites?
    • Analytics on events