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Spencer Killen 2023-01-19 10:53:15 -07:00
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lattices.ipynb
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@ -12,16 +12,16 @@
"- Very generic math structure\n", "- Very generic math structure\n",
"- For practical purposes: just a **finite** set with a subset relation\n", "- For practical purposes: just a **finite** set with a subset relation\n",
"- Paired with ``fixpoint operators``: functions that either\n", "- Paired with ``fixpoint operators``: functions that either\n",
" - Take a point and follow the lines upwards\n", " - Follow the lines upwards\n",
" - Stay in the same place\n", " - Stop\n",
"- Conditions above can be relaxed, but at the cost of complexity\n", "- Conditions above can be relaxed, but at the cost of complexity\n",
"\n", "\n",
"## Lattice programming\n", "## Lattice programming\n",
"- Partial solutions\n", "- Partial solutions\n",
"- Guaranteed termination\n", "- Guaranteed termination (through monotonicity)\n",
"- Very modular / elegant\n", "- Very modular / elegant\n",
"- A sane way to define recursive functions\n", "- Sane recursive functions - no induction\n",
"- Not an implementation, just an underlying theory to build upon\n", "- Theory, not implementation\n",
"\n", "\n",
"## Example Visualization\n", "## Example Visualization\n",
"\n" "\n"
@ -92,14 +92,10 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# Example Fixpoint Operator\n",
"\n",
"- Computation can start at the TOP or BOTTOM and move downwards or upwards in the lattice\n",
"- An operator is just a function that takes and element and moves in a direction consistently\n",
"\n", "\n",
"## Problem\n", "## Problem\n",
"\n", "\n",
"- A diagnostic approach to parts of speech tagging (POS tagging)\n", "- A diagnosis approach to parts of speech tagging (POS tagging)\n",
" - Diagnostics propose a tag, then possibly refute it\n", " - Diagnostics propose a tag, then possibly refute it\n",
"- POS: noun, verb, adverb, subject\n", "- POS: noun, verb, adverb, subject\n",
"### Lattice\n", "### Lattice\n",
@ -147,10 +143,8 @@
"\n", "\n",
"- Method stolen from classical linguistics ([uoa reference](https://ezpa.library.ualberta.ca/ezpAuthen.cgi?url=https://academic.oup.com/book/12008/chapter-abstract/161275349?redirectedFrom=fulltext)) ([non uoa, gated](https://academic.oup.com/book/12008/chapter/161275349?login=true))\n", "- Method stolen from classical linguistics ([uoa reference](https://ezpa.library.ualberta.ca/ezpAuthen.cgi?url=https://academic.oup.com/book/12008/chapter-abstract/161275349?redirectedFrom=fulltext)) ([non uoa, gated](https://academic.oup.com/book/12008/chapter/161275349?login=true))\n",
"- Rooted in generative grammar\n", "- Rooted in generative grammar\n",
"- Don't want to misrepresent it, its a lot more sophisticated than what I'm presenting here.\n", "- Simplified here\n",
"- General principle is apply rules to rule out possible interpretations\n", "- Operate on template sentences:\n",
"- I'm not an expert of linguistic diagnosis, I just think it's cool\n",
"- Given a template sentence, decide whether it's true when instantiated\n",
"- E.g. \"The dog kicked the ball\" -> (\"Who kicked the ball?\", \"Dog\") is true, then dog is NOUN(SUBJECT) \n", "- E.g. \"The dog kicked the ball\" -> (\"Who kicked the ball?\", \"Dog\") is true, then dog is NOUN(SUBJECT) \n",
"- Oracle-driven\n", "- Oracle-driven\n",
" - In classical linguistics, the linguist is the oracle\n", " - In classical linguistics, the linguist is the oracle\n",
@ -425,13 +419,11 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# Further Ideas\n", "# A fuzzier approach\n",
"## A fuzzier approach\n",
"\n", "\n",
"- We're expecting a lot from a our diagnostics to have to \"entirely refute\" a POS, a graded approach would be better\n", "- Binary deciding expects a lot from diagnostics\n",
"- That's possible!\n", "- Graded approach would be beter\n",
"- Now we have triples (word, tag, confidence) and give the diagnostics the ability to lower a confidence level\n", "- Modify to use triple (word: str, tag: str, confidence: float)\n"
"- But this is no longer a simple subset relation, so it needs more general-purpose lattice theory."
] ]
} }
], ],