From 35f91adcff95f5140bff8d85a13b42900506b419 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Pawe=C5=82=20Sk=C3=B3rzewski?= Date: Wed, 5 May 2021 15:23:24 +0200 Subject: [PATCH] Sieci neuronowe - propagacja wsteczna --- wyk/4_Sieci_neuronowe.ipynb | 1946 ++++++++++++++++++++++++++++++++++- wyk/exp1.png | Bin 0 -> 27700 bytes wyk/exp2.png | Bin 0 -> 75326 bytes wyk/multireglog.png | Bin 0 -> 57638 bytes wyk/nn1.png | Bin 0 -> 85282 bytes wyk/nn2.png | Bin 0 -> 87144 bytes wyk/nn3.png | Bin 0 -> 86587 bytes wyk/perceptron.png | Bin 0 -> 121613 bytes wyk/reglin.png | Bin 0 -> 165242 bytes wyk/reglog.png | Bin 0 -> 143531 bytes 10 files changed, 1932 insertions(+), 14 deletions(-) create mode 100644 wyk/exp1.png create mode 100644 wyk/exp2.png create mode 100644 wyk/multireglog.png create mode 100644 wyk/nn1.png create mode 100644 wyk/nn2.png create mode 100644 wyk/nn3.png create mode 100644 wyk/perceptron.png create mode 100644 wyk/reglin.png create mode 100644 wyk/reglog.png diff --git a/wyk/4_Sieci_neuronowe.ipynb b/wyk/4_Sieci_neuronowe.ipynb index d799edb..3863d5a 100644 --- a/wyk/4_Sieci_neuronowe.ipynb +++ b/wyk/4_Sieci_neuronowe.ipynb @@ -1259,7 +1259,433 @@ } }, "source": [ - "### Uczenie wielowarstwowych sieci neuronowych" + "### Jak uczyć sieci neuronowe?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* W poznanych do tej pory algorytmach (regresja liniowa, regresja logistyczna) do uczenia używaliśmy funkcji kosztu, jej gradientu oraz algorytmu gradientu prostego (GD/SGD)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Dla sieci neuronowych potrzebowalibyśmy również znaleźć gradient funkcji kosztu." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Sprowadza się to do bardziej ogólnego problemu:
jak obliczyć gradient $\\nabla f(x)$ dla danej funkcji $f$ i wektora wejściowego $x$?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 4.4. Metoda propagacji wstecznej – wprowadzenie" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Pochodna funkcji\n", + "\n", + "* **Pochodna** mierzy, jak szybko zmienia się wartość funkcji względem zmiany jej argumentów:\n", + "\n", + "$$ \\frac{d f(x)}{d x} = \\lim_{h \\to 0} \\frac{ f(x + h) - f(x) }{ h } $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Pochodna cząstkowa i gradient\n", + "\n", + "* **Pochodna cząstkowa** mierzy, jak szybko zmienia się wartość funkcji względem zmiany jej *pojedynczego argumentu*." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* **Gradient** to wektor pochodnych cząstkowych:\n", + "\n", + "$$ \\nabla f = \\left( \\frac{\\partial f}{\\partial x_1}, \\ldots, \\frac{\\partial f}{\\partial x_n} \\right) $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Gradient – przykłady" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$ f(x_1, x_2) = x_1 + x_2 \\qquad \\to \\qquad \\frac{\\partial f}{\\partial x_1} = 1, \\quad \\frac{\\partial f}{\\partial x_2} = 1, \\quad \\nabla f = (1, 1) $$ " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$ f(x_1, x_2) = x_1 \\cdot x_2 \\qquad \\to \\qquad \\frac{\\partial f}{\\partial x_1} = x_2, \\quad \\frac{\\partial f}{\\partial x_2} = x_1, \\quad \\nabla f = (x_2, x_1) $$ " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "$$ f(x_1, x_2) = \\max(x_1 + x_2) \\hskip{12em} \\\\\n", + "\\to \\qquad \\frac{\\partial f}{\\partial x_1} = \\mathbb{1}_{x \\geq y}, \\quad \\frac{\\partial f}{\\partial x_2} = \\mathbb{1}_{y \\geq x}, \\quad \\nabla f = (\\mathbb{1}_{x \\geq y}, \\mathbb{1}_{y \\geq x}) $$ " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Własności pochodnych cząstkowych\n", + "\n", + "Jezeli $f(x, y, z) = (x + y) \\, z$ oraz $x + y = q$, to:\n", + "$$f = q z,\n", + "\\quad \\frac{\\partial f}{\\partial q} = z,\n", + "\\quad \\frac{\\partial f}{\\partial z} = q,\n", + "\\quad \\frac{\\partial q}{\\partial x} = 1,\n", + "\\quad \\frac{\\partial q}{\\partial y} = 1 $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Reguła łańcuchowa\n", + "\n", + "$$ \\frac{\\partial f}{\\partial x} = \\frac{\\partial f}{\\partial q} \\, \\frac{\\partial q}{\\partial x},\n", + "\\quad \\frac{\\partial f}{\\partial y} = \\frac{\\partial f}{\\partial q} \\, \\frac{\\partial q}{\\partial y} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Propagacja wsteczna – prosty przykład" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# Dla ustalonego wejścia\n", + "x = -2; y = 5; z = -4" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(3, -12)\n" + ] + } + ], + "source": [ + "# Krok w przód\n", + "q = x + y\n", + "f = q * z\n", + "print(q, f)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-4, -4, 3]\n" + ] + } + ], + "source": [ + "# Propagacja wsteczna dla f = q * z\n", + "dz = q\n", + "dq = z\n", + "# Propagacja wsteczna dla q = x + y\n", + "dx = 1 * dq # z reguły łańcuchowej\n", + "dy = 1 * dq # z reguły łańcuchowej\n", + "print([dx, dy, dz])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Właśnie tak wygląda obliczanie pochodnych metodą propagacji wstecznej!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Spróbujmy czegoś bardziej skomplikowanego:
metodą propagacji wstecznej obliczmy pochodną funkcji sigmoidalnej." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Propagacja wsteczna – funkcja sigmoidalna" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Funkcja sigmoidalna:\n", + "\n", + "$$f(\\theta,x) = \\frac{1}{1+e^{-(\\theta_0 x_0 + \\theta_1 x_1 + \\theta_2)}}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "$$\n", + "\\begin{array}{lcl}\n", + "f(x) = \\frac{1}{x} \\quad & \\rightarrow & \\quad \\frac{df}{dx} = -\\frac{1}{x^2} \\\\\n", + "f_c(x) = c + x \\quad & \\rightarrow & \\quad \\frac{df}{dx} = 1 \\\\\n", + "f(x) = e^x \\quad & \\rightarrow & \\quad \\frac{df}{dx} = e^x \\\\\n", + "f_a(x) = ax \\quad & \\rightarrow & \\quad \\frac{df}{dx} = a \\\\\n", + "\\end{array}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.3932238664829637, -0.5898357997244456]\n", + "[-0.19661193324148185, -0.3932238664829637, 0.19661193324148185]\n" + ] + } + ], + "source": [ + "# Losowe wagi i dane\n", + "w = [2,-3,-3]\n", + "x = [-1, -2]\n", + "\n", + "# Krok w przód\n", + "dot = w[0]*x[0] + w[1]*x[1] + w[2]\n", + "f = 1.0 / (1 + math.exp(-dot)) # funkcja sigmoidalna\n", + "\n", + "# Krok w tył\n", + "ddot = (1 - f) * f # pochodna funkcji sigmoidalnej\n", + "dx = [w[0] * ddot, w[1] * ddot]\n", + "dw = [x[0] * ddot, x[1] * ddot, 1.0 * ddot]\n", + "\n", + "print(dx)\n", + "print(dw)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Obliczanie gradientów – podsumowanie" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Gradient $f$ dla $x$ mówi, jak zmieni się całe wyrażenie przy zmianie wartości $x$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Gradienty łączymy, korzystając z **reguły łańcuchowej**." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* W kroku \"wstecz\" gradienty informują, które części grafu powinny być zwiększone lub zmniejszone (i z jaką siłą), aby zwiększyć wartość na wyjściu." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* W kontekście implementacji chcemy dzielić funkcję $f$ na części, dla których można łatwo obliczyć gradienty." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 4.5. Uczenie wielowarstwowych sieci neuronowych metodą propagacji wstecznej" ] }, { @@ -1281,11 +1707,8 @@ } }, "source": [ - "* Niech:\n", - "$$\\Theta = (\\Theta^{(1)},\\Theta^{(2)},\\Theta^{(3)},\\beta^{(1)},\\beta^{(2)},\\beta^{(3)})$$\n", - "\n", + "* Niech $\\Theta = (\\Theta^{(1)},\\Theta^{(2)},\\Theta^{(3)},\\beta^{(1)},\\beta^{(2)},\\beta^{(3)})$\n", "* Funkcja sieci neuronowej z grafiki:\n", - "\n", "$$\\small h_\\Theta(x) = \\tanh(\\tanh(\\tanh(x\\Theta^{(1)}+\\beta^{(1)})\\Theta^{(2)} + \\beta^{(2)})\\Theta^{(3)} + \\beta^{(3)})$$\n", "* Funkcja kosztu dla regresji:\n", "$$J(\\Theta) = \\dfrac{1}{2m} \\sum_{i=1}^{m} (h_\\Theta(x^{(i)})- y^{(i)})^2 $$" @@ -1299,11 +1722,9 @@ } }, "source": [ - "Jak obliczymy gradienty?\n", + "* Jak obliczymy gradienty?\n", "\n", - "$$\\nabla_{\\Theta^{(l)}} J(\\Theta) = ? \\quad \\nabla_{\\beta^{(l)}} J(\\Theta) = ?$$\n", - "\n", - "* Postać funkcji kosztu zależna od wybranej architektury sieci oraz funkcji aktywacji." + "$$\\nabla_{\\Theta^{(l)}} J(\\Theta) = ? \\quad \\nabla_{\\beta^{(l)}} J(\\Theta) = ?$$" ] }, { @@ -1314,12 +1735,221 @@ } }, "source": [ - "$$\\small J(\\Theta) = \\frac{1}{2}(a^{(L)} - y)^2 $$\n", + "### W kierunku propagacji wstecznej\n", + "\n", + "* Pewna (niewielka) zmiana wagi $\\Delta z^l_j$ dla $j$-ego neuronu w warstwie $l$ pociąga za sobą (niewielką) zmianę kosztu: \n", + "\n", + "$$\\frac{\\partial J(\\Theta)}{\\partial z^{l}_j} \\Delta z^{l}_j$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Jeżeli $\\frac{\\partial J(\\Theta)}{\\partial z^{l}_j}$ jest duża, $\\Delta z^l_j$ ze znakiem przeciwnym zredukuje koszt.\n", + "* Jeżeli $\\frac{\\partial J(\\Theta)}{\\partial z^l_j}$ jest bliska zeru, koszt nie będzie mocno poprawiony." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Definiujemy błąd $\\delta^l_j$ neuronu $j$ w warstwie $l$: \n", + "\n", + "$$\\delta^l_j := \\dfrac{\\partial J(\\Theta)}{\\partial z^l_j}$$ \n", + "$$\\delta^l := \\nabla_{z^l} J(\\Theta) \\quad \\textrm{ (zapis wektorowy)} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Podstawowe równania propagacji wstecznej\n", + "\n", + "$$\n", + "\\begin{array}{rcll}\n", + "\\delta^L & = & \\nabla_{a^L}J(\\Theta) \\odot { \\left( g^{L} \\right) }^{\\prime} \\left( z^L \\right) & (BP1) \\\\[2mm]\n", + "\\delta^{l} & = & \\left( \\left( \\Theta^{l+1} \\right) \\! ^\\top \\, \\delta^{l+1} \\right) \\odot {{ \\left( g^{l} \\right) }^{\\prime}} \\left( z^{l} \\right) & (BP2)\\\\[2mm]\n", + "\\nabla_{\\beta^l} J(\\Theta) & = & \\delta^l & (BP3)\\\\[2mm]\n", + "\\nabla_{\\Theta^l} J(\\Theta) & = & a^{l-1} \\odot \\delta^l & (BP4)\\\\\n", + "\\end{array}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### (BP1)\n", + "$$ \\delta^L_j \\; = \\; \\frac{ \\partial J }{ \\partial a^L_j } \\, g' \\!\\! \\left( z^L_j \\right) $$\n", + "$$ \\delta^L \\; = \\; \\nabla_{a^L}J(\\Theta) \\odot { \\left( g^{L} \\right) }^{\\prime} \\left( z^L \\right) $$\n", + "Błąd w ostatniej warstwie jest iloczynem szybkości zmiany kosztu względem $j$-tego wyjścia i szybkości zmiany funkcji aktywacji w punkcie $z^L_j$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### (BP2)\n", + "$$ \\delta^{l} \\; = \\; \\left( \\left( \\Theta^{l+1} \\right) \\! ^\\top \\, \\delta^{l+1} \\right) \\odot {{ \\left( g^{l} \\right) }^{\\prime}} \\left( z^{l} \\right) $$\n", + "Aby obliczyć błąd w $l$-tej warstwie, należy przemnożyć błąd z następnej ($(l+1)$-szej) warstwy przez transponowany wektor wag, a uzyskaną macierz pomnożyć po współrzędnych przez szybkość zmiany funkcji aktywacji w punkcie $z^l$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### (BP3)\n", + "$$ \\nabla_{\\beta^l} J(\\Theta) \\; = \\; \\delta^l $$\n", + "Błąd w $l$-tej warstwie jest równy wartości gradientu funkcji kosztu." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### (BP4)\n", + "$$ \\nabla_{\\Theta^l} J(\\Theta) \\; = \\; a^{l-1} \\odot \\delta^l $$\n", + "Gradient funkcji kosztu względem wag $l$-tej warstwy można obliczyć jako iloczyn po współrzędnych $a^{l-1}$ przez $\\delta^l$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Algorytm propagacji wstecznej" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Dla pojedynczego przykładu $(x,y)$:\n", + "1. **Wejście**: Ustaw aktywacje w warstwie cech $a^{(0)}=x$ \n", + "2. **Feedforward:** dla $l=1,\\dots,L$ oblicz \n", + "$z^{(l)} = a^{(l-1)} \\Theta^{(l)} + \\beta^{(l)}$ oraz $a^{(l)}=g^{(l)} \\!\\! \\left( z^{(l)} \\right)$\n", + "3. **Błąd wyjścia $\\delta^{(L)}$:** oblicz wektor $$\\delta^{(L)}= \\nabla_{a^{(L)}}J(\\Theta) \\odot {g^{\\prime}}^{(L)} \\!\\! \\left( z^{(L)} \\right) $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "4. **Propagacja wsteczna błędu:** dla $l = L-1,L-2,\\dots,1$ oblicz $$\\delta^{(l)} = \\delta^{(l+1)}(\\Theta^{(l+1)})^T \\odot {g^{\\prime}}^{(l)} \\!\\! \\left( z^{(l)} \\right) $$\n", + "5. **Gradienty:** \n", + " * $\\dfrac{\\partial}{\\partial \\Theta_{ij}^{(l)}} J(\\Theta) = a_i^{(l-1)}\\delta_j^{(l)} \\textrm{ oraz } \\dfrac{\\partial}{\\partial \\beta_{j}^{(l)}} J(\\Theta) = \\delta_j^{(l)}$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "W naszym przykładzie:\n", + "\n", + "$$\\small J(\\Theta) = \\frac{1}{2} \\left( a^{(L)} - y \\right) ^2 $$\n", "$$\\small \\dfrac{\\partial}{\\partial a^{(L)}} J(\\Theta) = a^{(L)} - y$$\n", "\n", "$$\\small \\tanh^{\\prime}(x) = 1 - \\tanh^2(x)$$" ] }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Algorytm SGD z propagacją wsteczną\n", + "\n", + "Pojedyncza iteracja:\n", + "1. Dla parametrów $\\Theta = (\\Theta^{(1)},\\ldots,\\Theta^{(L)})$ utwórz pomocnicze macierze zerowe $\\Delta = (\\Delta^{(1)},\\ldots,\\Delta^{(L)})$ o takich samych wymiarach (dla uproszczenia opuszczono wagi $\\beta$)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "2. Dla $m$ przykładów we wsadzie (*batch*), $i = 1,\\ldots,m$:\n", + " * Wykonaj algortym propagacji wstecznej dla przykładu $(x^{(i)}, y^{(i)})$ i przechowaj gradienty $\\nabla_{\\Theta}J^{(i)}(\\Theta)$ dla tego przykładu;\n", + " * $\\Delta := \\Delta + \\dfrac{1}{m}\\nabla_{\\Theta}J^{(i)}(\\Theta)$\n", + "3. Wykonaj aktualizację wag: $\\Theta := \\Theta - \\alpha \\Delta$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Propagacja wsteczna – podsumowanie\n", + "\n", + "* Algorytm pierwszy raz wprowadzony w latach 70. XX w.\n", + "* W 1986 David Rumelhart, Geoffrey Hinton i Ronald Williams pokazali, że jest znacznie szybszy od wcześniejszych metod.\n", + "* Obecnie najpopularniejszy algorytm uczenia sieci neuronowych." + ] + }, { "cell_type": "markdown", "metadata": { @@ -1328,15 +1958,1303 @@ } }, "source": [ - "## 4.4. Metoda propagacji wstecznej – wprowadzenie" + "## 4.6. Implementacja sieci neuronowych" ] }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, + "execution_count": 6, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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\n", + "
" + ], + "text/plain": [ + " łod.dł. łod.sz. pł.dł. pł.sz. Iris setosa?\n", + "0 5.2 3.4 1.4 0.2 1.0\n", + "1 5.1 3.7 1.5 0.4 1.0\n", + "2 6.7 3.1 5.6 2.4 0.0\n", + "3 6.5 3.2 5.1 2.0 0.0\n", + "4 4.9 2.5 4.5 1.7 0.0\n", + "5 6.0 2.7 5.1 1.6 0.0" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas\n", + "src_cols = ['łod.dł.', 'łod.sz.', 'pł.dł.', 'pł.sz.', 'Gatunek']\n", + "trg_cols = ['łod.dł.', 'łod.sz.', 'pł.dł.', 'pł.sz.', 'Iris setosa?']\n", + "data = (\n", + " pandas.read_csv('iris.csv', usecols=src_cols)\n", + " .apply(lambda x: [x[0], x[1], x[2], x[3], 1 if x[4] == 'Iris-setosa' else 0], axis=1))\n", + "data.columns = trg_cols\n", + "data[:6]" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1. 5.2 3.4 1.4 0.2]\n", + " [1. 5.1 3.7 1.5 0.4]\n", + " [1. 6.7 3.1 5.6 2.4]\n", + " [1. 6.5 3.2 5.1 2. ]\n", + " [1. 4.9 2.5 4.5 1.7]\n", + " [1. 6. 2.7 5.1 1.6]]\n", + "[[1.]\n", + " [1.]\n", + " [0.]\n", + " [0.]\n", + " [0.]\n", + " [0.]]\n" + ] + } + ], + "source": [ + "m, n_plus_1 = data.values.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data.values[:, 0:n].reshape(m, n)\n", + "X = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n", + "Y = np.matrix(data.values[:, n]).reshape(m, 1)\n", + "\n", + "print(X[:6])\n", + "print(Y[:6])" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "scrolled": true, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/pawel/.local/lib/python2.7/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", + " from ._conv import register_converters as _register_converters\n", + "Using TensorFlow backend.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 1/1\n", + "150/150 [==============================] - 0s 2ms/step - loss: 3.6282 - acc: 0.3333\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from keras.models import Sequential\n", + "from keras.layers import Dense\n", + "\n", + "model = Sequential()\n", + "model.add(Dense(3, input_dim=5))\n", + "model.add(Dense(3))\n", + "model.add(Dense(1, activation='sigmoid'))\n", + "\n", + "model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy'])\n", + "\n", + "model.fit(X, Y)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.05484907701611519" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.predict(np.array([1.0, 3.0, 1.0, 2.0, 4.0]).reshape(-1, 5)).tolist()[0][0]" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "150/150 [==============================] - 0s 293us/step\n", + "()\n", + "loss:\t3.4469\n", + "acc:\t0.3333\n" + ] + } + ], + "source": [ + "scores = model.evaluate(X, Y)\n", + "print()\n", + "for i in range(len(scores)):\n", + " print('{}:\\t{:.4f}'.format(model.metrics_names[i], scores[i]))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 4.7. Przykłady implementacji wielowarstwowych sieci neuronowych" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Przykład: MNIST\n", + "\n", + "_Modified National Institute of Standards and Technology database_" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Zbiór cyfr zapisanych pismem odręcznym\n", + "* 60 000 przykładów uczących, 10 000 przykładów testowych\n", + "* Rozdzielczość każdego przykładu: 28 × 28 = 784 piksele" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, "outputs": [], - "source": [] + "source": [ + "# źródło: https://github.com/keras-team/keras/examples/minst_mlp.py\n", + "\n", + "import keras\n", + "from keras.datasets import mnist\n", + "\n", + "# załaduj dane i podziel je na zbiory uczący i testowy\n", + "(x_train, y_train), (x_test, y_test) = mnist.load_data()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def draw_examples(examples, captions=None):\n", + " plt.figure(figsize=(16, 4))\n", + " m = len(examples)\n", + " for i, example in enumerate(examples):\n", + " plt.subplot(100 + m * 10 + i + 1)\n", + " plt.imshow(example, cmap=plt.get_cmap('gray'))\n", + " plt.show()\n", + " if captions is not None:\n", + " print(6 * ' ' + (10 * ' ').join(str(captions[i]) for i in range(m)))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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Cf6ypA+ogl2vBRAYOAAAAAIATnKwIAAAAAOAUE1EAAAAAgFNMRAEAAAAATjER\nBQAAAAA4xUQUAAAAAOAUE1EAAAAAgFNMRAEAAAAATv0/VRGGEPckXi4AAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 5 0 4 1 9 2 1\n" + ] + } + ], + "source": [ + "draw_examples(x_train[:7], captions=y_train)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "60000 przykładów uczących\n", + "10000 przykładów testowych\n" + ] + } + ], + "source": [ + "num_classes = 10\n", + "\n", + "x_train = x_train.reshape(60000, 784) # 784 = 28 * 28\n", + "x_test = x_test.reshape(10000, 784)\n", + "x_train = x_train.astype('float32')\n", + "x_test = x_test.astype('float32')\n", + "x_train /= 255\n", + "x_test /= 255\n", + "print('{} przykładów uczących'.format(x_train.shape[0]))\n", + "print('{} przykładów testowych'.format(x_test.shape[0]))\n", + "\n", + "# przekonwertuj wektory klas na binarne macierze klas\n", + "y_train = keras.utils.to_categorical(y_train, num_classes)\n", + "y_test = keras.utils.to_categorical(y_test, num_classes)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "scrolled": true, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "_________________________________________________________________\n", + "Layer (type) Output Shape Param # \n", + "=================================================================\n", + "dense_1 (Dense) (None, 512) 401920 \n", + "_________________________________________________________________\n", + "dropout_1 (Dropout) (None, 512) 0 \n", + "_________________________________________________________________\n", + "dense_2 (Dense) (None, 512) 262656 \n", + "_________________________________________________________________\n", + "dropout_2 (Dropout) (None, 512) 0 \n", + "_________________________________________________________________\n", + "dense_3 (Dense) (None, 10) 5130 \n", + "=================================================================\n", + "Total params: 669,706\n", + "Trainable params: 669,706\n", + "Non-trainable params: 0\n", + "_________________________________________________________________\n" + ] + } + ], + "source": [ + "model = Sequential()\n", + "model.add(Dense(512, activation='relu', input_shape=(784,)))\n", + "model.add(Dropout(0.2))\n", + "model.add(Dense(512, activation='relu'))\n", + "model.add(Dropout(0.2))\n", + "model.add(Dense(num_classes, activation='softmax'))\n", + "model.summary()" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "((60000, 784), (60000, 10))\n" + ] + } + ], + "source": [ + "print(x_train.shape, y_train.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Train on 60000 samples, validate on 10000 samples\n", + "Epoch 1/5\n", + "60000/60000 [==============================] - 9s 153us/step - loss: 0.2489 - acc: 0.9224 - val_loss: 0.1005 - val_acc: 0.9706\n", + "Epoch 2/5\n", + "60000/60000 [==============================] - 9s 151us/step - loss: 0.1042 - acc: 0.9683 - val_loss: 0.0861 - val_acc: 0.9740\n", + "Epoch 3/5\n", + "60000/60000 [==============================] - 9s 153us/step - loss: 0.0742 - acc: 0.9782 - val_loss: 0.0733 - val_acc: 0.9796\n", + "Epoch 4/5\n", + "60000/60000 [==============================] - 9s 154us/step - loss: 0.0603 - acc: 0.9824 - val_loss: 0.0713 - val_acc: 0.9800\n", + "Epoch 5/5\n", + "60000/60000 [==============================] - 9s 157us/step - loss: 0.0512 - acc: 0.9848 - val_loss: 0.0749 - val_acc: 0.9795\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.compile(loss='categorical_crossentropy', optimizer=RMSprop(), metrics=['accuracy'])\n", + "\n", + "model.fit(x_train, y_train, batch_size=128, epochs=5, verbose=1,\n", + " validation_data=(x_test, y_test))" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test loss: 0.074858742202\n", + "Test accuracy: 0.9795\n" + ] + } + ], + "source": [ + "score = model.evaluate(x_test, y_test, verbose=0)\n", + "\n", + "print('Test loss: {}'.format(score[0]))\n", + "print('Test accuracy: {}'.format(score[1]))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Warstwa _dropout_ to metoda regularyzacji, służy zapobieganiu nadmiernemu dopasowaniu sieci. Polega na tym, że część węzłów sieci jest usuwana w sposób losowy." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "_________________________________________________________________\n", + "Layer (type) Output Shape Param # \n", + "=================================================================\n", + "dense_4 (Dense) (None, 512) 401920 \n", + "_________________________________________________________________\n", + "dense_5 (Dense) (None, 512) 262656 \n", + "_________________________________________________________________\n", + "dense_6 (Dense) (None, 10) 5130 \n", + "=================================================================\n", + "Total params: 669,706\n", + "Trainable params: 669,706\n", + "Non-trainable params: 0\n", + "_________________________________________________________________\n", + "Train on 60000 samples, validate on 10000 samples\n", + "Epoch 1/5\n", + "60000/60000 [==============================] - 8s 139us/step - loss: 0.2237 - acc: 0.9303 - val_loss: 0.0998 - val_acc: 0.9676\n", + "Epoch 2/5\n", + "60000/60000 [==============================] - 8s 136us/step - loss: 0.0818 - acc: 0.9748 - val_loss: 0.0788 - val_acc: 0.9770\n", + "Epoch 3/5\n", + "60000/60000 [==============================] - 8s 136us/step - loss: 0.0538 - acc: 0.9831 - val_loss: 0.1074 - val_acc: 0.9695\n", + "Epoch 4/5\n", + "60000/60000 [==============================] - 10s 161us/step - loss: 0.0397 - acc: 0.9879 - val_loss: 0.0871 - val_acc: 0.9763\n", + "Epoch 5/5\n", + "60000/60000 [==============================] - 12s 195us/step - loss: 0.0299 - acc: 0.9910 - val_loss: 0.0753 - val_acc: 0.9812\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Bez warstw Dropout\n", + "\n", + "num_classes = 10\n", + "\n", + "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n", + "\n", + "x_train = x_train.reshape(60000, 784) # 784 = 28 * 28\n", + "x_test = x_test.reshape(10000, 784)\n", + "x_train = x_train.astype('float32')\n", + "x_test = x_test.astype('float32')\n", + "x_train /= 255\n", + "x_test /= 255\n", + "\n", + "y_train = keras.utils.to_categorical(y_train, num_classes)\n", + "y_test = keras.utils.to_categorical(y_test, num_classes)\n", + "\n", + "model_no_dropout = Sequential()\n", + "model_no_dropout.add(Dense(512, activation='relu', input_shape=(784,)))\n", + "model_no_dropout.add(Dense(512, activation='relu'))\n", + "model_no_dropout.add(Dense(num_classes, activation='softmax'))\n", + "model_no_dropout.summary()\n", + "\n", + "model_no_dropout.compile(loss='categorical_crossentropy',\n", + " optimizer=RMSprop(),\n", + " metrics=['accuracy'])\n", + "\n", + "model_no_dropout.fit(x_train, y_train,\n", + " batch_size=128,\n", + " epochs=5,\n", + " verbose=1,\n", + " validation_data=(x_test, y_test))" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test loss (no dropout): 0.0753162465898\n", + "Test accuracy (no dropout): 0.9812\n" + ] + } + ], + "source": [ + "# Bez warstw Dropout\n", + "\n", + "score = model_no_dropout.evaluate(x_test, y_test, verbose=0)\n", + "\n", + "print('Test loss (no dropout): {}'.format(score[0]))\n", + "print('Test accuracy (no dropout): {}'.format(score[1]))" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "_________________________________________________________________\n", + "Layer (type) Output Shape Param # \n", + "=================================================================\n", + "dense_7 (Dense) (None, 2500) 1962500 \n", + "_________________________________________________________________\n", + "dense_8 (Dense) (None, 2000) 5002000 \n", + "_________________________________________________________________\n", + "dense_9 (Dense) (None, 1500) 3001500 \n", + "_________________________________________________________________\n", + "dense_10 (Dense) (None, 1000) 1501000 \n", + "_________________________________________________________________\n", + "dense_11 (Dense) (None, 500) 500500 \n", + "_________________________________________________________________\n", + "dense_12 (Dense) (None, 10) 5010 \n", + "=================================================================\n", + "Total params: 11,972,510\n", + "Trainable params: 11,972,510\n", + "Non-trainable params: 0\n", + "_________________________________________________________________\n", + "Train on 60000 samples, validate on 10000 samples\n", + "Epoch 1/10\n", + "60000/60000 [==============================] - 145s 2ms/step - loss: 1.4242 - acc: 0.5348 - val_loss: 0.4426 - val_acc: 0.8638\n", + "Epoch 2/10\n", + "60000/60000 [==============================] - 140s 2ms/step - loss: 0.3245 - acc: 0.9074 - val_loss: 0.2231 - val_acc: 0.9360\n", + "Epoch 3/10\n", + "60000/60000 [==============================] - 137s 2ms/step - loss: 0.1993 - acc: 0.9420 - val_loss: 0.1694 - val_acc: 0.9485\n", + "Epoch 4/10\n", + "60000/60000 [==============================] - 136s 2ms/step - loss: 0.1471 - acc: 0.9571 - val_loss: 0.1986 - val_acc: 0.9381\n", + "Epoch 5/10\n", + "60000/60000 [==============================] - 132s 2ms/step - loss: 0.1189 - acc: 0.9650 - val_loss: 0.1208 - val_acc: 0.9658\n", + "Epoch 6/10\n", + "60000/60000 [==============================] - 131s 2ms/step - loss: 0.0983 - acc: 0.9711 - val_loss: 0.1260 - val_acc: 0.9637\n", + "Epoch 7/10\n", + "60000/60000 [==============================] - 129s 2ms/step - loss: 0.0818 - acc: 0.9753 - val_loss: 0.0984 - val_acc: 0.9727\n", + "Epoch 8/10\n", + "60000/60000 [==============================] - 129s 2ms/step - loss: 0.0710 - acc: 0.9784 - val_loss: 0.1406 - val_acc: 0.9597\n", + "Epoch 9/10\n", + "60000/60000 [==============================] - 129s 2ms/step - loss: 0.0611 - acc: 0.9811 - val_loss: 0.0987 - val_acc: 0.9727\n", + "Epoch 10/10\n", + "60000/60000 [==============================] - 136s 2ms/step - loss: 0.0533 - acc: 0.9837 - val_loss: 0.1070 - val_acc: 0.9718\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Więcej warstw, inna funkcja aktywacji\n", + "\n", + "num_classes = 10\n", + "\n", + "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n", + "\n", + "x_train = x_train.reshape(60000, 784) # 784 = 28 * 28\n", + "x_test = x_test.reshape(10000, 784)\n", + "x_train = x_train.astype('float32')\n", + "x_test = x_test.astype('float32')\n", + "x_train /= 255\n", + "x_test /= 255\n", + "\n", + "y_train = keras.utils.to_categorical(y_train, num_classes)\n", + "y_test = keras.utils.to_categorical(y_test, num_classes)\n", + "\n", + "model3 = Sequential()\n", + "model3.add(Dense(2500, activation='tanh', input_shape=(784,)))\n", + "model3.add(Dense(2000, activation='tanh'))\n", + "model3.add(Dense(1500, activation='tanh'))\n", + "model3.add(Dense(1000, activation='tanh'))\n", + "model3.add(Dense(500, activation='tanh'))\n", + "model3.add(Dense(num_classes, activation='softmax'))\n", + "model3.summary()\n", + "\n", + "model3.compile(loss='categorical_crossentropy',\n", + " optimizer=RMSprop(),\n", + " metrics=['accuracy'])\n", + "\n", + "model3.fit(x_train, y_train,\n", + " batch_size=128,\n", + " epochs=10,\n", + " verbose=1,\n", + " validation_data=(x_test, y_test))" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test loss: 0.107020105763\n", + "Test accuracy: 0.9718\n" + ] + } + ], + "source": [ + "# Więcej warstw, inna funkcja aktywacji\n", + "\n", + "score = model3.evaluate(x_test, y_test, verbose=0)\n", + "\n", + "print('Test loss: {}'.format(score[0]))\n", + "print('Test accuracy: {}'.format(score[1]))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Przykład: 4-pikselowy aparat fotograficzny\n", + "\n", + "https://www.youtube.com/watch?v=ILsA4nyG7I0" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "def generate_example(description):\n", + " variant = random.choice([1, -1])\n", + " if description == 's': # solid\n", + " return (np.array([[ 1.0, 1.0], [ 1.0, 1.0]]) if variant == 1 else\n", + " np.array([[-1.0, -1.0], [-1.0, -1.0]]))\n", + " elif description == 'v': # vertical\n", + " return (np.array([[ 1.0, -1.0], [ 1.0, -1.0]]) if variant == 1 else\n", + " np.array([[-1.0, 1.0], [-1.0, 1.0]]))\n", + " elif description == 'd': # diagonal\n", + " return (np.array([[ 1.0, -1.0], [-1.0, 1.0]]) if variant == 1 else\n", + " np.array([[-1.0, 1.0], [ 1.0, -1.0]]))\n", + " elif description == 'h': # horizontal\n", + " return (np.array([[ 1.0, 1.0], [-1.0, -1.0]]) if variant == 1 else\n", + " np.array([[-1.0, -1.0], [ 1.0, 1.0]]))\n", + " else:\n", + " return np.array([[random.uniform(-1, 1), random.uniform(-1, 1)],\n", + " [random.uniform(-1, 1), random.uniform(-1, 1)]])" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "num_classes = 4\n", + "\n", + "trainset_size = 4000\n", + "testset_size = 1000\n", + "\n", + "y4_train = np.array([random.choice(['s', 'v', 'd', 'h']) for i in range(trainset_size)])\n", + "x4_train = np.array([generate_example(desc) for desc in y4_train])\n", + "\n", + "y4_test = np.array([random.choice(['s', 'v', 'd', 'h']) for i in range(testset_size)])\n", + "x4_test = np.array([generate_example(desc) for desc in y4_test])" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " s s d s h s v\n" + ] + } + ], + "source": [ + "draw_examples(x4_train[:7], captions=y4_train)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "x4_train = x4_train.reshape(trainset_size, 4)\n", + "x4_test = x4_test.reshape(testset_size, 4)\n", + "x4_train = x4_train.astype('float32')\n", + "x4_test = x4_test.astype('float32')\n", + "\n", + "y4_train = np.array([{'s': 0, 'v': 1, 'd': 2, 'h': 3}[desc] for desc in y4_train])\n", + "y4_test = np.array([{'s': 0, 'v': 1, 'd': 2, 'h': 3}[desc] for desc in y4_test])\n", + "\n", + "y4_train = keras.utils.to_categorical(y4_train, num_classes)\n", + "y4_test = keras.utils.to_categorical(y4_test, num_classes)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "_________________________________________________________________\n", + "Layer (type) Output Shape Param # \n", + "=================================================================\n", + "dense_16 (Dense) (None, 4) 20 \n", + "_________________________________________________________________\n", + "dense_17 (Dense) (None, 4) 20 \n", + "_________________________________________________________________\n", + "dense_18 (Dense) (None, 8) 40 \n", + "_________________________________________________________________\n", + "dense_19 (Dense) (None, 4) 36 \n", + "=================================================================\n", + "Total params: 116\n", + "Trainable params: 116\n", + "Non-trainable params: 0\n", + "_________________________________________________________________\n" + ] + } + ], + "source": [ + "model4 = Sequential()\n", + "model4.add(Dense(4, activation='tanh', input_shape=(4,)))\n", + "model4.add(Dense(4, activation='tanh'))\n", + "model4.add(Dense(8, activation='relu'))\n", + "model4.add(Dense(num_classes, activation='softmax'))\n", + "model4.summary()" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "model4.layers[0].set_weights(\n", + " [np.array([[ 1.0, 0.0, 1.0, 0.0],\n", + " [ 0.0, 1.0, 0.0, 1.0],\n", + " [ 1.0, 0.0, -1.0, 0.0],\n", + " [ 0.0, 1.0, 0.0, -1.0]],\n", + " dtype=np.float32), np.array([0., 0., 0., 0.], dtype=np.float32)])\n", + "model4.layers[1].set_weights(\n", + " [np.array([[ 1.0, -1.0, 0.0, 0.0],\n", + " [ 1.0, 1.0, 0.0, 0.0],\n", + " [ 0.0, 0.0, 1.0, -1.0],\n", + " [ 0.0, 0.0, -1.0, -1.0]],\n", + " dtype=np.float32), np.array([0., 0., 0., 0.], dtype=np.float32)])\n", + "model4.layers[2].set_weights(\n", + " [np.array([[ 1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n", + " [ 0.0, 0.0, 1.0, -1.0, 0.0, 0.0, 0.0, 0.0],\n", + " [ 0.0, 0.0, 0.0, 0.0, 1.0, -1.0, 0.0, 0.0],\n", + " [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -1.0]],\n", + " dtype=np.float32), np.array([0., 0., 0., 0., 0., 0., 0., 0.], dtype=np.float32)])" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "model4.layers[3].set_weights(\n", + " [np.array([[ 1.0, 0.0, 0.0, 0.0],\n", + " [ 1.0, 0.0, 0.0, 0.0],\n", + " [ 0.0, 1.0, 0.0, 0.0],\n", + " [ 0.0, 1.0, 0.0, 0.0],\n", + " [ 0.0, 0.0, 1.0, 0.0],\n", + " [ 0.0, 0.0, 1.0, 0.0],\n", + " [ 0.0, 0.0, 0.0, 1.0],\n", + " [ 0.0, 0.0, 0.0, 1.0]],\n", + " dtype=np.float32), np.array([0., 0., 0., 0.], dtype=np.float32)])\n", + "\n", + "model4.compile(loss='categorical_crossentropy',\n", + " optimizer=Adagrad(),\n", + " metrics=['accuracy'])" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[array([[ 1., 0., 1., 0.],\n", + " [ 0., 1., 0., 1.],\n", + " [ 1., 0., -1., 0.],\n", + " [ 0., 1., 0., -1.]], dtype=float32), array([ 0., 0., 0., 0.], dtype=float32)]\n", + "[array([[ 1., -1., 0., 0.],\n", + " [ 1., 1., 0., 0.],\n", + " [ 0., 0., 1., -1.],\n", + " [ 0., 0., -1., -1.]], dtype=float32), array([ 0., 0., 0., 0.], dtype=float32)]\n", + "[array([[ 1., -1., 0., 0., 0., 0., 0., 0.],\n", + " [ 0., 0., 1., -1., 0., 0., 0., 0.],\n", + " [ 0., 0., 0., 0., 1., -1., 0., 0.],\n", + " [ 0., 0., 0., 0., 0., 0., 1., -1.]], dtype=float32), array([ 0., 0., 0., 0., 0., 0., 0., 0.], dtype=float32)]\n", + "[array([[ 1., 0., 0., 0.],\n", + " [ 1., 0., 0., 0.],\n", + " [ 0., 1., 0., 0.],\n", + " [ 0., 1., 0., 0.],\n", + " [ 0., 0., 1., 0.],\n", + " [ 0., 0., 1., 0.],\n", + " [ 0., 0., 0., 1.],\n", + " [ 0., 0., 0., 1.]], dtype=float32), array([ 0., 0., 0., 0.], dtype=float32)]\n" + ] + } + ], + "source": [ + "for layer in model4.layers:\n", + " print(layer.get_weights())" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.17831734, 0.17831734, 0.17831734, 0.46504799]], dtype=float32)" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model4.predict([np.array([[1.0, 1.0], [-1.0, -1.0]]).reshape(1, 4)])" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test loss: 0.765614629269\n", + "Test accuracy: 1.0\n" + ] + } + ], + "source": [ + "score = model4.evaluate(x4_test, y4_test, verbose=0)\n", + "\n", + "print('Test loss: {}'.format(score[0]))\n", + "print('Test accuracy: {}'.format(score[1]))" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "_________________________________________________________________\n", + "Layer (type) Output Shape Param # \n", + "=================================================================\n", + "dense_20 (Dense) (None, 4) 20 \n", + "_________________________________________________________________\n", + "dense_21 (Dense) (None, 4) 20 \n", + "_________________________________________________________________\n", + "dense_22 (Dense) (None, 8) 40 \n", + "_________________________________________________________________\n", + "dense_23 (Dense) (None, 4) 36 \n", + "=================================================================\n", + "Total params: 116\n", + "Trainable params: 116\n", + "Non-trainable params: 0\n", + "_________________________________________________________________\n" + ] + } + ], + "source": [ + "model5 = Sequential()\n", + "model5.add(Dense(4, activation='tanh', input_shape=(4,)))\n", + "model5.add(Dense(4, activation='tanh'))\n", + "model5.add(Dense(8, activation='relu'))\n", + "model5.add(Dense(num_classes, activation='softmax'))\n", + "model5.compile(loss='categorical_crossentropy',\n", + " optimizer=RMSprop(),\n", + " metrics=['accuracy'])\n", + "model5.summary()" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "scrolled": true, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Train on 4000 samples, validate on 1000 samples\n", + "Epoch 1/8\n", + "4000/4000 [==============================] - 0s - loss: 1.1352 - acc: 0.5507 - val_loss: 1.0160 - val_acc: 0.7330\n", + "Epoch 2/8\n", + "4000/4000 [==============================] - 0s - loss: 0.8918 - acc: 0.8722 - val_loss: 0.8094 - val_acc: 0.8580\n", + "Epoch 3/8\n", + "4000/4000 [==============================] - 0s - loss: 0.6966 - acc: 0.8810 - val_loss: 0.6283 - val_acc: 0.8580\n", + "Epoch 4/8\n", + "4000/4000 [==============================] - 0s - loss: 0.5284 - acc: 0.8810 - val_loss: 0.4697 - val_acc: 0.8580\n", + "Epoch 5/8\n", + "4000/4000 [==============================] - 0s - loss: 0.3797 - acc: 0.9022 - val_loss: 0.3312 - val_acc: 1.0000\n", + "Epoch 6/8\n", + "4000/4000 [==============================] - 0s - loss: 0.2555 - acc: 1.0000 - val_loss: 0.2166 - val_acc: 1.0000\n", + "Epoch 7/8\n", + "4000/4000 [==============================] - 0s - loss: 0.1612 - acc: 1.0000 - val_loss: 0.1318 - val_acc: 1.0000\n", + "Epoch 8/8\n", + "4000/4000 [==============================] - 0s - loss: 0.0939 - acc: 1.0000 - val_loss: 0.0732 - val_acc: 1.0000\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model5.fit(x4_train, y4_train, epochs=8, validation_data=(x4_test, y4_test))" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.00708295, 0.00192736, 0.02899081, 0.96199888]], dtype=float32)" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model5.predict([np.array([[1.0, 1.0], [-1.0, -1.0]]).reshape(1, 4)])" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test loss: 0.0731911802292\n", + "Test accuracy: 1.0\n" + ] + } + ], + "source": [ + "score = model5.evaluate(x4_test, y4_test, verbose=0)\n", + "\n", + "print('Test loss: {}'.format(score[0]))\n", + "print('Test accuracy: {}'.format(score[1]))" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "import contextlib\n", + "\n", + "@contextlib.contextmanager\n", + "def printoptions(*args, **kwargs):\n", + " original = np.get_printoptions()\n", + " np.set_printoptions(*args, **kwargs)\n", + " try:\n", + " yield\n", + " finally: \n", + " np.set_printoptions(**original)" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "scrolled": true, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[array([[-0.2, -0.5, 0.8, 1. ],\n", + " [-0.9, 0.1, -0.8, 0.2],\n", + " [-0.2, 0.4, 0.1, -0.4],\n", + " [-0.8, 0.8, 1. , 0.3]], dtype=float32), array([ 0. , -0. , 0.1, -0.1], dtype=float32)]\n", + "[array([[-0.4, 0.9, -1.3, 1.7],\n", + " [-0.4, -0.7, 0.3, -0.3],\n", + " [ 0.8, -0.9, -1.1, -0.2],\n", + " [ 1.3, 0.5, 0.4, -0.2]], dtype=float32), array([-0. , -0. , 0.2, 0. ], dtype=float32)]\n", + "[array([[-1.6, 0.3, 0.3, -0.3, -1.1, 1.2, 0.7, -1. ],\n", + " [ 0.4, 1.3, -0.9, 0.8, -0.4, -0.7, -1.2, -1. ],\n", + " [ 0.6, 1. , 0.9, -1. , -1.1, -0.2, -0.4, -0.3],\n", + " [ 1.1, 0.1, -0.9, 1.3, -0.3, -0.2, 0.2, -0.4]], dtype=float32), array([-0. , 0.2, -0.1, 0. , -0.1, -0. , -0.1, 0.1], dtype=float32)]\n", + "[array([[ 0.6, -1.5, 1.3, -1.4],\n", + " [-0.4, -1.6, -0.3, 1.2],\n", + " [ 1.2, 1.1, -0.3, -1.5],\n", + " [ 0.6, 1.4, -1.5, -1.2],\n", + " [ 0.2, -1.3, -0.9, 0.8],\n", + " [ 0.6, -1.5, 0.8, -1. ],\n", + " [ 0.4, -1.3, 0.4, 0.3],\n", + " [-1.3, 0.5, -0.9, 0.8]], dtype=float32), array([-0.8, 0.7, 0.4, 0.1], dtype=float32)]\n" + ] + } + ], + "source": [ + "with printoptions(precision=1, suppress=True):\n", + " for layer in model5.layers:\n", + " print(layer.get_weights())" + ] } ], "metadata": { diff --git a/wyk/exp1.png b/wyk/exp1.png new file mode 100644 index 0000000000000000000000000000000000000000..8d8c14658ea68c4d8648ab12355d7d5776da27d7 GIT binary patch literal 27700 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