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Modelowanie języka

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7. Zanurzenia słów [wykład]

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09. Zanurzenia słów (Word2vec) [wykład]

\n", "

Filip Graliński (2022)

\n", "\n", "\n", @@ -19,7 +19,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Zanurzenia słów\n", + "## Zanurzenia słów (Word2vec)\n", "\n" ] }, @@ -122,7 +122,7 @@ "po prostu będziemy rozpatrywać $|V|$ najczęstszych wyrazów, pozostałe zamienimy\n", "na specjalny token `` reprezentujący nieznany (*unknown*) wyraz.\n", "\n", - "Aby utworzyć taki słownik użyjemy gotowej klasy `Vocab` z pakietu torchtext:\n", + "Aby utworzyć taki słownik, użyjemy gotowej klasy `Vocab` z pakietu torchtext:\n", "\n" ] }, @@ -313,33 +313,48 @@ "next(iter(DataLoader(train_dataset, batch_size=5)))" ] }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "None" + ] + } + ], + "source": [ + "device = 'cuda'\n", + "model = SimpleBigramNeuralLanguageModel(vocab_size, embed_size).to(device)\n", + "data = DataLoader(train_dataset, batch_size=5000)\n", + "optimizer = torch.optim.Adam(model.parameters())\n", + "criterion = torch.nn.NLLLoss()\n", + "\n", + "model.train()\n", + "step = 0\n", + "for x, y in data:\n", + " x = x.to(device)\n", + " y = y.to(device)\n", + " optimizer.zero_grad()\n", + " ypredicted = model(x)\n", + " loss = criterion(torch.log(ypredicted), y)\n", + " if step % 100 == 0:\n", + " print(step, loss)\n", + " step += 1\n", + " loss.backward()\n", + " optimizer.step()\n", + "\n", + "torch.save(model.state_dict(), 'model1.bin')" + ] + }, { "cell_type": "markdown", "metadata": {}, "source": [ - " device = 'cuda'\n", - " model = SimpleBigramNeuralLanguageModel(vocab_size, embed_size).to(device)\n", - " data = DataLoader(train_dataset, batch_size=5000)\n", - " optimizer = torch.optim.Adam(model.parameters())\n", - " criterion = torch.nn.NLLLoss()\n", - " \n", - " model.train()\n", - " step = 0\n", - " for x, y in data:\n", - " x = x.to(device)\n", - " y = y.to(device)\n", - " optimizer.zero_grad()\n", - " ypredicted = model(x)\n", - " loss = criterion(torch.log(ypredicted), y)\n", - " if step % 100 == 0:\n", - " print(step, loss)\n", - " step += 1\n", - " loss.backward()\n", - " optimizer.step()\n", - " \n", - " torch.save(model.state_dict(), 'model1.bin')\n", - "\n", - "Policzmy najbardziej prawdopodobne kontynuację dla zadanego słowa:\n", + "Policzmy najbardziej prawdopodobne kontynuacje dla zadanego słowa:\n", "\n" ] }, @@ -502,7 +517,7 @@ "warstwy liniowej, naszą sieć możemy interpretować jako jednowarstwową\n", "sieć neuronową, co można zilustrować za pomocą następującego diagramu:\n", "\n", - "![img](./07_Zanurzenia_slow/bigram1.drawio.png \"Diagram prostego bigramowego neuronowego modelu języka\")\n", + "![img](./09_Zanurzenia_slow/bigram1.drawio.png \"Diagram prostego bigramowego neuronowego modelu języka\")\n", "\n" ] }, @@ -535,7 +550,7 @@ "\n", "W postaci diagramu można tę interpretację zilustrować w następujący sposób:\n", "\n", - "![img](./07_Zanurzenia_slow/bigram2.drawio.png \"Diagram prostego bigramowego neuronowego modelu języka z wejściem w postaci one-hot\")\n", + "![img](./09_Zanurzenia_slow/bigram2.drawio.png \"Diagram prostego bigramowego neuronowego modelu języka z wejściem w postaci one-hot\")\n", "\n" ] } @@ -556,7 +571,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.10.2" + "version": "3.10.5" }, "org": null }, diff --git a/wyk/07_Zanurzenia_slow.org b/wyk/09_Zanurzenia_slow.org similarity index 91% rename from wyk/07_Zanurzenia_slow.org rename to wyk/09_Zanurzenia_slow.org index f4c6a42..94352b1 100644 --- a/wyk/07_Zanurzenia_slow.org +++ b/wyk/09_Zanurzenia_slow.org @@ -1,4 +1,4 @@ -* Zanurzenia słów +* Zanurzenia słów (Word2vec) W praktyce stosowalność słowosieci okazała się zaskakująco ograniczona. Większy przełom w przetwarzaniu języka naturalnego przyniosły @@ -47,9 +47,9 @@ ograniczony. Zazwyczaj jest to liczba rzędu kilkudziesięciu wyrazów — po prostu będziemy rozpatrywać $|V|$ najczęstszych wyrazów, pozostałe zamienimy na specjalny token ~~ reprezentujący nieznany (/unknown/) wyraz. -Aby utworzyć taki słownik użyjemy gotowej klasy ~Vocab~ z pakietu torchtext: +Aby utworzyć taki słownik, użyjemy gotowej klasy ~Vocab~ z pakietu torchtext: -#+BEGIN_SRC python :session mysession :exports both :results raw drawer +#+BEGIN_SRC ipython :session mysession :exports both :results raw drawer from itertools import islice import regex as re import sys @@ -84,7 +84,7 @@ Aby utworzyć taki słownik użyjemy gotowej klasy ~Vocab~ z pakietu torchtext: 16 :end: -#+BEGIN_SRC python :session mysession :exports both :results raw drawer +#+BEGIN_SRC ipython :session mysession :exports both :results raw drawer vocab.lookup_tokens([0, 1, 2, 10, 12345]) #+END_SRC @@ -97,7 +97,7 @@ vocab.lookup_tokens([0, 1, 2, 10, 12345]) Naszą prostą sieć neuronową zaimplementujemy używając frameworku PyTorch. -#+BEGIN_SRC python :session mysession :exports both :results raw drawer +#+BEGIN_SRC ipython :session mysession :exports both :results raw drawer from torch import nn import torch @@ -132,7 +132,7 @@ Teraz wyuczmy model. Wpierw tylko potasujmy nasz plik: shuf < opensubtitlesA.pl.txt > opensubtitlesA.pl.shuf.txt #+END_SRC -#+BEGIN_SRC python :session mysession :exports both :results raw drawer +#+BEGIN_SRC ipython :session mysession :exports both :results raw drawer from torch.utils.data import IterableDataset import itertools @@ -164,7 +164,7 @@ shuf < opensubtitlesA.pl.txt > opensubtitlesA.pl.shuf.txt :results: :end: -#+BEGIN_SRC python :session mysession :exports both :results raw drawer +#+BEGIN_SRC ipython :session mysession :exports both :results raw drawer from torch.utils.data import DataLoader next(iter(train_dataset)) @@ -175,7 +175,7 @@ shuf < opensubtitlesA.pl.txt > opensubtitlesA.pl.shuf.txt (2, 5) :end: -#+BEGIN_SRC python :session mysession :exports both :results raw drawer +#+BEGIN_SRC ipython :session mysession :exports both :results raw drawer from torch.utils.data import DataLoader next(iter(DataLoader(train_dataset, batch_size=5))) @@ -186,7 +186,7 @@ shuf < opensubtitlesA.pl.txt > opensubtitlesA.pl.shuf.txt [tensor([ 2, 5, 51, 3481, 231]), tensor([ 5, 51, 3481, 231, 4])] :end: -#+BEGIN_SRC python :session mysession :exports both :results raw drawer +#+BEGIN_SRC ipython :session mysession :exports both :results raw drawer device = 'cuda' model = SimpleBigramNeuralLanguageModel(vocab_size, embed_size).to(device) data = DataLoader(train_dataset, batch_size=5000) @@ -215,9 +215,9 @@ shuf < opensubtitlesA.pl.txt > opensubtitlesA.pl.shuf.txt None :end: -Policzmy najbardziej prawdopodobne kontynuację dla zadanego słowa: +Policzmy najbardziej prawdopodobne kontynuacje dla zadanego słowa: -#+BEGIN_SRC python :session mysession :exports both :results raw drawer +#+BEGIN_SRC ipython :session mysession :exports both :results raw drawer device = 'cuda' model = SimpleBigramNeuralLanguageModel(vocab_size, embed_size).to(device) model.load_state_dict(torch.load('model1.bin')) @@ -240,7 +240,7 @@ Policzmy najbardziej prawdopodobne kontynuację dla zadanego słowa: Teraz zbadajmy najbardziej podobne zanurzenia dla zadanego słowa: -#+BEGIN_SRC python :session mysession :exports both :results raw drawer +#+BEGIN_SRC ipython :session mysession :exports both :results raw drawer vocab = train_dataset.vocab ixs = torch.tensor(vocab.forward(['kłopot'])).to(device) @@ -257,7 +257,7 @@ Teraz zbadajmy najbardziej podobne zanurzenia dla zadanego słowa: [('.', 3, 0.404473215341568), (',', 4, 0.14222915470600128), ('z', 14, 0.10945753753185272), ('?', 6, 0.09583134204149246), ('w', 10, 0.050338443368673325), ('na', 12, 0.020703863352537155), ('i', 11, 0.016762692481279373), ('', 0, 0.014571071602404118), ('...', 15, 0.01453721895813942), ('', 1, 0.011769450269639492)] :end: -#+BEGIN_SRC python :session mysession :exports both :results raw drawer +#+BEGIN_SRC ipython :session mysession :exports both :results raw drawer cos = nn.CosineSimilarity(dim=1, eps=1e-6) embeddings = model.model[0].weight @@ -313,7 +313,7 @@ warstwy liniowej, naszą sieć możemy interpretować jako jednowarstwową sieć neuronową, co można zilustrować za pomocą następującego diagramu: #+CAPTION: Diagram prostego bigramowego neuronowego modelu języka -[[./07_Zanurzenia_slow/bigram1.drawio.png]] +[[./09_Zanurzenia_slow/bigram1.drawio.png]] *** Zanurzenie jako mnożenie przez macierz @@ -335,4 +335,4 @@ gdzie $E$ będzie tym razem macierzą $m \times |V|$. W postaci diagramu można tę interpretację zilustrować w następujący sposób: #+CAPTION: Diagram prostego bigramowego neuronowego modelu języka z wejściem w postaci one-hot -[[./07_Zanurzenia_slow/bigram2.drawio.png]] +[[./09_Zanurzenia_slow/bigram2.drawio.png]] diff --git a/wyk/10_Neuronowy_ngramowy_model.ipynb b/wyk/10_Neuronowy_ngramowy_model.ipynb index 3131aaa..c9416d6 100644 --- a/wyk/10_Neuronowy_ngramowy_model.ipynb +++ b/wyk/10_Neuronowy_ngramowy_model.ipynb @@ -1,4 +1,3 @@ - { "cells": [ { @@ -16,4 +15,355 @@ "\n" ] }, -{"cell_type":"markdown","metadata":{},"source":["## Neuronowy n-gramowy model języka\n\n"]},{"cell_type":"markdown","metadata":{},"source":["Omówiony w poprzedniej części neuronowy bigramowy model języka\nwarunkuje kolejny wyraz jedynie względem bezpośrednio poprzedzającego\n— jak w każdym bigramowym modelu przyjmujemy założenie, że $w_i$\nzależy tylko od $w_{i-1}$. Rzecz jasna jest to bardzo duże\nograniczenie, w rzeczywistości bardzo często prawdopodobieństwo\nkolejnego wyrazu zależy od wyrazu dwie, trzy, cztery itd. pozycje\nwstecz czy w ogólności od wszystkich wyrazów poprzedzających (bez\nwzględu na ich pozycje).\n\n**Pytanie**: Wskaż zależności o zasięgu większym niż 1 wyraz w zdaniu\n/Zatopieni w kłębach dymu cygar i pochyleni nad butelkami z ciemnego\nszkła obywatele tej dzielnicy, jedni zakładali się o wygranę lub\nprzegranę Anglii, drudzy o bankructwo Wokulskiego; jedni nazywali\ngeniuszem Bismarcka, drudzy — awanturnikiem Wokulskiego; jedni\nkrytykowali postępowanie prezydenta MacMahona, inni twierdzili, że\nWokulski jest zdecydowanym wariatem, jeżeli nie czymś gorszym…/\n\n"]},{"cell_type":"markdown","metadata":{},"source":["### Trigramowy neuronowy model języka\n\n"]},{"cell_type":"markdown","metadata":{},"source":["Spróbujmy najpierw rozszerzyć nasz model na trigramy, to znaczy\nbędziemy przewidywać słowo $w_i$ na podstawie słów $w_{i-2}$ i\n$w_{i-1}$.\n\nNajprostsze rozwiązanie polegałoby na zanurzeniu pary $(w_{i-2},\nw_{i-1})$ w całości i postępowaniu jak w przypadku modelu bigramowego.\nByłoby to jednak zupełnie niepraktyczne, jako że:\n\n- liczba zanurzeń do wyuczenia byłaby olbrzymia ($|V|^2$ — byłoby to\n ewentualnie akceptowalne dla modeli operujących na krótszych\n jednostkach niż słowa, np. na znakach),\n- w szczególności zanurzenia dla par $(v, u)$, $(u, v)$, $(u, u)$ i\n $(v, v)$ nie miałyby ze sobą nic wspólnego.\n\n"]},{"cell_type":"markdown","metadata":{},"source":["#### Konketanacja zanurzeń\n\n"]},{"cell_type":"markdown","metadata":{},"source":["Właściwsze rozwiązanie polega na zanurzeniu dalej pojedynczych słów i\nnastępnie ich **konkatenowaniu**.\n\nPrzypomnijmy, że konkatenacja wektorów $\\vec{x_1}$ i $\\vec{x_2}$ to wektor o rozmiarze\n$|\\vec{x_1}| + |\\vec{x_2}|$ powstały ze „sklejania” wektorów $\\vec{x_1}$ i $\\vec{x_2}$.\nKonkatenację wektorów $\\vec{x_1}$ i $\\vec{x_2}$ będziemy oznaczać za pomocą $[\\vec{x_1}, \\vec{x_2}]$.\n\nPrzykład: jeśli $\\vec{x_1} = [-1, 2, 0]$ i $\\vec{x_2} = [3, -3]$,\nwówczas $[\\vec{x_1}, \\vec{x_2}] = [-1, 2, 0, 3, -3]$\n\nOznacza to, że nasza macierz „kontekstowa” $C$ powinna mieć w modelu trigramowym rozmiar nie\n$|V| \\times m$, lecz $|V| \\times (m+m)$ = $|V| \\times 2m$ i wyjście będzie zdefiniowane za pomocą wzoru:\n\n$$\\vec{y} = \\operatorname{softmax}(C[E(w_{i-2}),E(w_{i-1})]),$$\n\nco można przedstawić za pomocą następującego schematu:\n\n![img](./10_Neuronowy_ngramowy_model/trigram1.drawio.png \"Diagram prostego bigramowego neuronowego modelu języka\")\n\n"]},{"cell_type":"markdown","metadata":{},"source":["##### Rozbicie macierzy $C$\n\n"]},{"cell_type":"markdown","metadata":{},"source":["Zamiast mnożyć macierz $C$ przez konkatenację dwóch wektorów, można\nrozbić macierz $C$ na dwie, powiedzmy $C_{-2}$ i $C_{-1}$, przemnażać\nje osobno przez odpowiadające im wektory i następnie **dodać** macierze,\ntak aby:\n\n$$C[E(w_{i-2}),E(w_{i-1})] = C_{-2}E(w_{i-2}) + C_{-1}E(w_{i-1}).$$\n\nMacierze $C_{-2}$ i $C_{-1}$ będą miały rozmiar $|V| \\times m$.\n\nPrzy tym podejściu możemy powiedzieć, że ostatni i przedostatni wyraz\nmają swoje osobne macierze o potencjalnie różnych wagach — co ma sens,\njako że na inne aspekty zwracamy uwagę przewidując kolejne słowo na\npodstawie wyrazu bezpośrednio poprzedzającego, a na inne — na\npodstawie słowa występującego dwie pozycje wcześniej.\n\n"]},{"cell_type":"markdown","metadata":{},"source":["### Uogólnienie na $n$-gramowy model języka dla dowolnego $n$\n\n"]},{"cell_type":"markdown","metadata":{},"source":["Łatwo uogólnić opisany wyżej trigramowy model języka dla dowolnego $n$.\nUogólniony model można przedstawić za pomocą wzoru:\n\n$$\\vec{y} = \\operatorname{softmax}(C[E(w_{i-n+1}),\\dots,E(w_{i-1})]),$$\n\ngdzie macierz $C$ ma rozmiar $|V| \\times nm$ lub za pomocą wzoru:\n\n$$\\vec{y} = \\operatorname{softmax}(C_{-(n-1)}E(w_{i-n+1}) + \\dots + C_{-1}E(w_{i-1}),$$\n\ngdzie macierze $C_{-(n-1)}$, …, $C_{-1}$ mają rozmiary $|V| \\times m$.\n\nPor. diagram:\n\n![img](./10_Neuronowy_ngramowy_model/ngram.drawio.png \"Diagram prostego n-gramowego neuronowego modelu języka\")\n\n"]},{"cell_type":"markdown","metadata":{},"source":["### Dodanie kolejnej warstwy\n\n"]},{"cell_type":"markdown","metadata":{},"source":["W wypadku trigramowego czy — ogólniej — n-gramowego modelu języka dla\n$n \\geq 3$ warto dodać kolejną (**ukrytą**) warstwę, na którą będziemy rzutować\nskonkatenowane embeddingi, zanim zrzutujemy je do długiego wektora\nprawdopodobieństw.\n\nZakładamy, że warstwa ukryta zawiera $h$ neuronów. Wartość $h$ powinna być mniejsza\nniż $nm$ (a może nawet od $m$).\n\n**Pytanie**: Dlaczego wartość $h > nm$ nie jest racjonalnym wyborem?\n\n**Pytanie**: Dlaczego dodanie kolejnej warstwy nie ma sensu dla modelu bigramowego?\n\n"]},{"cell_type":"markdown","metadata":{},"source":["#### Funkcja aktywacji\n\n"]},{"cell_type":"markdown","metadata":{},"source":["Aby warstwa ukryta wnosiła coś nowego, na wyjściu z tej funkcji musimy (dlaczego?)\nzastosować nieliniową **funkcji aktywacji**. Zazwyczaj jako funkcji\naktywacji w sieciach neuronowych używa się funkcji ReLU albo funkcji\nsigmoidalnej. W prostych neuronowych modelach języka sprawdza się też\n**tangens hiperboliczny** (tgh, w literaturze anglojęzycznej tanh):\n\n$$\\operatorname{tgh}(x) = \\frac{e^x - e^{-x}}{e^x + e^{-x}}.$$\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":""},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\nimport torch\nimport torch.nn as nn\n\nx = torch.linspace(-5,5,100)\nplt.xlabel(\"x\")\nplt.ylabel(\"y\")\na = torch.Tensor(x.size()[0]).fill_(2.)\nm = torch.stack([x, a])\nplt.plot(x, nn.functional.tanh(m)[0])\nfname = '10_Neuronowy_ngramowy_model/tanh.png'\nplt.savefig(fname)\nfname"]},{"cell_type":"markdown","metadata":{},"source":["##### Tangens hiperboliczny zastosowany dla wektora\n\n"]},{"cell_type":"markdown","metadata":{},"source":["Tangens hiperboliczny wektora będzie po prostu wektorem tangensów\nhiperbolicznych poszczególnych wartości.\n\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["import torch\nimport torch.nn as nn\n\nv = torch.Tensor([-100, -2.0, 0.0, 0.5, 1000.0])\nnn.functional.tanh(v)"]},{"cell_type":"markdown","metadata":{},"source":["[[[tensor](tensor)([-1.0000, -0.9640, 0.0000, 0.4621, 1.0000])]]\n\n"]},{"cell_type":"markdown","metadata":{},"source":["#### Wzór i schemat dwuwarstwowego n-gramowego neuronowego modelu języka\n\n"]},{"cell_type":"markdown","metadata":{},"source":["Dwuwarstwowy model języka będzie określony następującym wzorem:\n\n$$\\vec{y} = \\operatorname{softmax}(C\\operatorname{tgh}(W[E(w_{i-n+1}),\\dots,E(w_{i-1})])),$$\n\ngdzie:\n\n- $W$ jest wyuczalną macierzą wag o rozmiarze $h \\times nm$,\n- $C$ będzie macierzą o rozmiarze $|V| \\times h$.\n\nZmodyfikowaną sieć można przedstawić za pomocą następującego schematu:\n\n![img](./10_Neuronowy_ngramowy_model/ngram-tgh.drawio.png \"Dwuwarstwowy n-gramowy neuronowy model języka\")\n\n"]},{"cell_type":"markdown","metadata":{},"source":["#### Liczba wag w modelu dwuwarstwowym\n\n"]},{"cell_type":"markdown","metadata":{},"source":["Na wagi w modelu dwuwarstwowym składają się:\n\n- zanurzenia: $m|V|$,\n- wagi warstwy ukrytej: $hnm$,\n- wagi warstwy wyjściowej: $|V|h$,\n\na zatem łącznie:\n\n$$m|V| + hnm + |V|h$$\n\nJeśli $h \\approx m$ (co jest realistyczną opcją), wówczas otrzymamy oszacowanie:\n\n$$O(m|V| + nm^2).$$\n\nZauważmy, że względem $n$ oznacza to bardzo korzystną złożoność\n$O(n)$! Oznacza to, że nasz model może działać dla dużo większych\nwartości $n$ niż tradycyjny, statystyczny n-gramowy model języka (dla którego\nwartości $n > 5$ zazwyczaj nie mają sensu).\n\n"]}],"metadata":{"org":null,"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.5.2"}},"nbformat":4,"nbformat_minor":0} \ No newline at end of file + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Neuronowy n-gramowy model języka\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Omówiony w poprzedniej części neuronowy bigramowy model języka\n", + "warunkuje kolejny wyraz jedynie względem bezpośrednio poprzedzającego\n", + "— jak w każdym bigramowym modelu przyjmujemy założenie, że $w_i$\n", + "zależy tylko od $w_{i-1}$. Rzecz jasna jest to bardzo duże\n", + "ograniczenie, w rzeczywistości bardzo często prawdopodobieństwo\n", + "kolejnego wyrazu zależy od wyrazu dwie, trzy, cztery itd. pozycje\n", + "wstecz czy w ogólności od wszystkich wyrazów poprzedzających (bez\n", + "względu na ich pozycje).\n", + "\n", + "**Pytanie**: Wskaż zależności o zasięgu większym niż 1 wyraz w zdaniu\n", + "/Zatopieni w kłębach dymu cygar i pochyleni nad butelkami z ciemnego\n", + "szkła obywatele tej dzielnicy, jedni zakładali się o wygranę lub\n", + "przegranę Anglii, drudzy o bankructwo Wokulskiego; jedni nazywali\n", + "geniuszem Bismarcka, drudzy — awanturnikiem Wokulskiego; jedni\n", + "krytykowali postępowanie prezydenta MacMahona, inni twierdzili, że\n", + "Wokulski jest zdecydowanym wariatem, jeżeli nie czymś gorszym…/\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Trigramowy neuronowy model języka\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Spróbujmy najpierw rozszerzyć nasz model na trigramy, to znaczy\n", + "będziemy przewidywać słowo $w_i$ na podstawie słów $w_{i-2}$ i\n", + "$w_{i-1}$.\n", + "\n", + "Najprostsze rozwiązanie polegałoby na zanurzeniu pary $(w_{i-2},\n", + "w_{i-1})$ w całości i postępowaniu jak w przypadku modelu bigramowego.\n", + "Byłoby to jednak zupełnie niepraktyczne, jako że:\n", + "\n", + "- liczba zanurzeń do wyuczenia byłaby olbrzymia ($|V|^2$ — byłoby to\n", + " ewentualnie akceptowalne dla modeli operujących na krótszych\n", + " jednostkach niż słowa, np. na znakach),\n", + "- w szczególności zanurzenia dla par $(v, u)$, $(u, v)$, $(u, u)$ i\n", + " $(v, v)$ nie miałyby ze sobą nic wspólnego.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Konketanacja zanurzeń\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Właściwsze rozwiązanie polega na zanurzeniu dalej pojedynczych słów i\n", + "następnie ich **konkatenowaniu**.\n", + "\n", + "Przypomnijmy, że konkatenacja wektorów $\\vec{x_1}$ i $\\vec{x_2}$ to wektor o rozmiarze\n", + "$|\\vec{x_1}| + |\\vec{x_2}|$ powstały ze „sklejania” wektorów $\\vec{x_1}$ i $\\vec{x_2}$.\n", + "Konkatenację wektorów $\\vec{x_1}$ i $\\vec{x_2}$ będziemy oznaczać za pomocą $[\\vec{x_1}, \\vec{x_2}]$.\n", + "\n", + "Przykład: jeśli $\\vec{x_1} = [-1, 2, 0]$ i $\\vec{x_2} = [3, -3]$,\n", + "wówczas $[\\vec{x_1}, \\vec{x_2}] = [-1, 2, 0, 3, -3]$\n", + "\n", + "Oznacza to, że nasza macierz „kontekstowa” $C$ powinna mieć w modelu trigramowym rozmiar nie\n", + "$|V| \\times m$, lecz $|V| \\times (m+m)$ = $|V| \\times 2m$ i wyjście będzie zdefiniowane za pomocą wzoru:\n", + "\n", + "$$\\vec{y} = \\operatorname{softmax}(C[E(w_{i-2}),E(w_{i-1})]),$$\n", + "\n", + "co można przedstawić za pomocą następującego schematu:\n", + "\n", + "![img](./10_Neuronowy_ngramowy_model/trigram1.drawio.png \"Diagram prostego bigramowego neuronowego modelu języka\")\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Rozbicie macierzy $C$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Zamiast mnożyć macierz $C$ przez konkatenację dwóch wektorów, można\n", + "rozbić macierz $C$ na dwie, powiedzmy $C_{-2}$ i $C_{-1}$, przemnażać\n", + "je osobno przez odpowiadające im wektory i następnie **dodać** macierze,\n", + "tak aby:\n", + "\n", + "$$C[E(w_{i-2}),E(w_{i-1})] = C_{-2}E(w_{i-2}) + C_{-1}E(w_{i-1}).$$\n", + "\n", + "Macierze $C_{-2}$ i $C_{-1}$ będą miały rozmiar $|V| \\times m$.\n", + "\n", + "Przy tym podejściu możemy powiedzieć, że ostatni i przedostatni wyraz\n", + "mają swoje osobne macierze o potencjalnie różnych wagach — co ma sens,\n", + "jako że na inne aspekty zwracamy uwagę przewidując kolejne słowo na\n", + "podstawie wyrazu bezpośrednio poprzedzającego, a na inne — na\n", + "podstawie słowa występującego dwie pozycje wcześniej.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Uogólnienie na $n$-gramowy model języka dla dowolnego $n$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Łatwo uogólnić opisany wyżej trigramowy model języka dla dowolnego $n$.\n", + "Uogólniony model można przedstawić za pomocą wzoru:\n", + "\n", + "$$\\vec{y} = \\operatorname{softmax}(C[E(w_{i-n+1}),\\dots,E(w_{i-1})]),$$\n", + "\n", + "gdzie macierz $C$ ma rozmiar $|V| \\times nm$ lub za pomocą wzoru:\n", + "\n", + "$$\\vec{y} = \\operatorname{softmax}(C_{-(n-1)}E(w_{i-n+1}) + \\dots + C_{-1}E(w_{i-1}),$$\n", + "\n", + "gdzie macierze $C_{-(n-1)}$, …, $C_{-1}$ mają rozmiary $|V| \\times m$.\n", + "\n", + "Por. diagram:\n", + "\n", + "![img](./10_Neuronowy_ngramowy_model/ngram.drawio.png \"Diagram prostego n-gramowego neuronowego modelu języka\")\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Dodanie kolejnej warstwy\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "W wypadku trigramowego czy — ogólniej — n-gramowego modelu języka dla\n", + "$n \\geq 3$ warto dodać kolejną (**ukrytą**) warstwę, na którą będziemy rzutować\n", + "skonkatenowane embeddingi, zanim zrzutujemy je do długiego wektora\n", + "prawdopodobieństw.\n", + "\n", + "Zakładamy, że warstwa ukryta zawiera $h$ neuronów. Wartość $h$ powinna być mniejsza\n", + "niż $nm$ (a może nawet od $m$).\n", + "\n", + "**Pytanie**: Dlaczego wartość $h > nm$ nie jest racjonalnym wyborem?\n", + "\n", + "**Pytanie**: Dlaczego dodanie kolejnej warstwy nie ma sensu dla modelu bigramowego?\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Funkcja aktywacji\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Aby warstwa ukryta wnosiła coś nowego, na wyjściu z tej funkcji musimy (dlaczego?)\n", + "zastosować nieliniową **funkcji aktywacji**. Zazwyczaj jako funkcji\n", + "aktywacji w sieciach neuronowych używa się funkcji ReLU albo funkcji\n", + "sigmoidalnej. W prostych neuronowych modelach języka sprawdza się też\n", + "**tangens hiperboliczny** (tgh, w literaturze anglojęzycznej tanh):\n", + "\n", + "$$\\operatorname{tgh}(x) = \\frac{e^x - e^{-x}}{e^x + e^{-x}}.$$\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import torch\n", + "import torch.nn as nn\n", + "\n", + "x = torch.linspace(-5,5,100)\n", + "plt.xlabel(\"x\")\n", + "plt.ylabel(\"y\")\n", + "a = torch.Tensor(x.size()[0]).fill_(2.)\n", + "m = torch.stack([x, a])\n", + "plt.plot(x, nn.functional.tanh(m)[0])\n", + "fname = '10_Neuronowy_ngramowy_model/tanh.png'\n", + "plt.savefig(fname)\n", + "fname" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Tangens hiperboliczny zastosowany dla wektora\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Tangens hiperboliczny wektora będzie po prostu wektorem tangensów\n", + "hiperbolicznych poszczególnych wartości.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import torch\n", + "import torch.nn as nn\n", + "\n", + "v = torch.Tensor([-100, -2.0, 0.0, 0.5, 1000.0])\n", + "nn.functional.tanh(v)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[[[tensor](tensor)([-1.0000, -0.9640, 0.0000, 0.4621, 1.0000])]]\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Wzór i schemat dwuwarstwowego n-gramowego neuronowego modelu języka\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Dwuwarstwowy model języka będzie określony następującym wzorem:\n", + "\n", + "$$\\vec{y} = \\operatorname{softmax}(C\\operatorname{tgh}(W[E(w_{i-n+1}),\\dots,E(w_{i-1})])),$$\n", + "\n", + "gdzie:\n", + "\n", + "- $W$ jest wyuczalną macierzą wag o rozmiarze $h \\times nm$,\n", + "- $C$ będzie macierzą o rozmiarze $|V| \\times h$.\n", + "\n", + "Zmodyfikowaną sieć można przedstawić za pomocą następującego schematu:\n", + "\n", + "![img](./10_Neuronowy_ngramowy_model/ngram-tgh.drawio.png \"Dwuwarstwowy n-gramowy neuronowy model języka\")\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Liczba wag w modelu dwuwarstwowym\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Na wagi w modelu dwuwarstwowym składają się:\n", + "\n", + "- zanurzenia: $m|V|$,\n", + "- wagi warstwy ukrytej: $hnm$,\n", + "- wagi warstwy wyjściowej: $|V|h$,\n", + "\n", + "a zatem łącznie:\n", + "\n", + "$$m|V| + hnm + |V|h$$\n", + "\n", + "Jeśli $h \\approx m$ (co jest realistyczną opcją), wówczas otrzymamy oszacowanie:\n", + "\n", + "$$O(m|V| + nm^2).$$\n", + "\n", + "Zauważmy, że względem $n$ oznacza to bardzo korzystną złożoność\n", + "$O(n)$! Oznacza to, że nasz model może działać dla dużo większych\n", + "wartości $n$ niż tradycyjny, statystyczny n-gramowy model języka (dla którego\n", + "wartości $n > 5$ zazwyczaj nie mają sensu).\n", + "\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.5" + }, + "org": null + }, + "nbformat": 4, + "nbformat_minor": 1 +}