| … | … | @@ -105,7 +105,10 @@ Linas Vepštas |
| 105 | 105 | |
| 106 | 106 | \begin_layout Abstract |
| 107 | 107 | Diary entry, attempting to work out some ideas. |
| 108 | | |
| 108 | Wrttten in pseudo–chronological order. |
| 109 | Stream–of–consciousness, kind of. |
| 110 | Moving forward, I hope. |
| 111 | Maybe going in circles. |
| 109 | 112 | \end_layout |
| 110 | 113 | |
| 111 | 114 | \begin_layout Section* |
| … | … | @@ -372,8 +375,81 @@ The symbolic learning project is to determine the lexis automatically. |
| 372 | 375 | Or an old idea or a new idea. |
| 373 | 376 | \end_layout |
| 374 | 377 | |
| 378 | \begin_layout Section* |
| 379 | Corpus Model |
| 380 | \end_layout |
| 381 | |
| 375 | 382 | \begin_layout Standard |
| 376 | 383 | So, first, define a corpus: a collection of sentences. |
| 384 | For the moment, let this be |
| 385 | \begin_inset Quotes eld |
| 386 | \end_inset |
| 387 | |
| 388 | bag of sentences |
| 389 | \begin_inset Quotes erd |
| 390 | \end_inset |
| 391 | |
| 392 | , in jumbled order. |
| 393 | A |
| 394 | \begin_inset Quotes eld |
| 395 | \end_inset |
| 396 | |
| 397 | sentence |
| 398 | \begin_inset Quotes erd |
| 399 | \end_inset |
| 400 | |
| 401 | double be a dozen words. |
| 402 | But it could also be an ordered sequence of 100K words, i.e. |
| 403 | a book, article, newspaper story, twitter/bluesky post, whatever. |
| 404 | The length is immaterial; instead, we just take a collection of them, assumed |
| 405 | to be independent. |
| 406 | For now. |
| 407 | Of course, ten books written on the same topic are not really independent |
| 408 | of one-another, but lets not get ahead of ourselves. |
| 409 | \end_layout |
| 410 | |
| 411 | \begin_layout Standard |
| 412 | The corpus is |
| 413 | \begin_inset Formula $\mathcal{C}=\left\{ S_{i}\right\} $ |
| 414 | \end_inset |
| 415 | |
| 416 | which is a set of sentences |
| 417 | \begin_inset Formula $S_{i}$ |
| 418 | \end_inset |
| 419 | |
| 420 | labelled with some index |
| 421 | \begin_inset Formula $i$ |
| 422 | \end_inset |
| 423 | |
| 424 | . |
| 425 | There is a total of |
| 426 | \begin_inset Formula $\left|\mathcal{C}\right|$ |
| 427 | \end_inset |
| 428 | |
| 429 | sentences, where |
| 430 | \begin_inset Formula $\left|\cdot\right|$ |
| 431 | \end_inset |
| 432 | |
| 433 | denotes the size (cardinal) of a set. |
| 434 | The Hamiltonian is then |
| 435 | \begin_inset Formula |
| 436 | \[ |
| 437 | \mathcal{H}=\sum_{S_{i}\in\mathcal{C}}H\left(S_{i}\right) |
| 438 | \] |
| 439 | |
| 440 | \end_inset |
| 441 | |
| 442 | where the sum ranges over all sentences in the corpus, and |
| 443 | \begin_inset Formula $H\left(S_{i}\right)$ |
| 444 | \end_inset |
| 445 | |
| 446 | is the total cost of the parse (linkage) of that sentence. |
| 447 | \end_layout |
| 448 | |
| 449 | \begin_layout Standard |
| 450 | And so here we meet our first conceptual problem: the linkage is not unique: |
| 451 | any given sentence may have many linkages, and, in fact, we have to consdier, |
| 452 | in principle, all possible linkages. |
| 377 | 453 | \end_layout |
| 378 | 454 | |
| 379 | 455 | \begin_layout Section* |