Neural-Networks-From-Scratch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Networks\n",
    "\n",
    "* Neural network is a function which takes a vector $\\mathbf x$ with $n$ elements and produces an output $\\mathbf y$ with $n_{ \\mathrm out}$ elements\n",
    "* Assume to have have $N$ samples of $\\mathbf x$ and $\\mathbf y$.\n",
    "* For neural networks is it generally required to have a large sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Test\n",
    "using PyPlot\n",
    "using Random\n",
    "using LinearAlgebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×1000 Array{Float64,2}:\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  …  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0     0.0  0.0  0.0  0.0  0.0  0.0  0.0"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 1000; # number of samples\n",
    "n = 2; # number of features\n",
    "nout = 2\n",
    "x = randn(n,N)\n",
    "y = zeros(nout,N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try some random function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "f(x) = x[1,:] .+ x[2,:] + 2. ./ (x[1,:].^2 .+ x[2,:].^2 .+ 0.3);\n",
    "y[1,:] =f(x);\n",
    "\n",
    "y[2,:] = x[1,:] .- x[2,:];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot this function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xmin = [-3, -3]\n",
    "xmax = [3, 3]\n",
    "\n",
    "gx = [px for px = range(xmin[1],stop=xmax[1],length=100), py = range(xmin[2],stop=xmax[2],length=100)]\n",
    "gy = [py for px = range(xmin[1],stop=xmax[1],length=100), py = range(xmin[2],stop=xmax[2],length=100)]\n",
    "\n",
    "gf = reshape(f([gx[:]'; gy[:]']),size(gx))\n",
    "pcolor(gx,gy,gf);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the number of neurons in each layer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.collections.PathCollection object at 0x7fc056e1dac8>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#plot(x[1,:],x[2,:],\"k.\"; markersize = 1)\n",
    "scatter(x[1,:],x[2,:],4,y[1,:])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Int64,1}:\n",
       "  2\n",
       " 20\n",
       " 20\n",
       "  2"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Random.seed!(123)\n",
    "nneurons = [n,20,20,nout]\n",
    "\n",
    "\n",
    "#w = [randn(10,n),randn(nout,10)]\n",
    "#b = [randn(10), randn(nout)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialize the weights and biases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "function randnomwb(nneurons)\n",
    "  w = Matrix{Float64}[]\n",
    "  b = Vector{Float64}[]\n",
    "\n",
    "  for i = 2:length(nneurons)\n",
    "    push!(w,randn(nneurons[i],nneurons[i-1]))\n",
    "    push!(b,randn(nneurons[i]))    \n",
    "  end\n",
    "    \n",
    "  return w,b\n",
    "end\n",
    "\n",
    "w,b = randnomwb(nneurons);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Tuple{Int64},1}:\n",
       " (20,)\n",
       " (20,)\n",
       " (2,) "
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size.(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Activation functions and their derivative"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(∇sigmoid(0), (sigmoid(0.001) - sigmoid(0)) / 0.001) = (0.25, 0.2499999791666374)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "∇relu (generic function with 1 method)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmoid(x) = 1/(1+exp(-x))\n",
    "∇sigmoid(x) = exp(-x)/(1+exp(-x))^2\n",
    "\n",
    "@show ∇sigmoid(0), (sigmoid(0.001) - sigmoid(0)) / 0.001\n",
    "\n",
    "relu(x) = max(x,zero(x))\n",
    "∇relu(x) = (x > 0 ? one(x) : zero(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xplot = -3:0.1:3\n",
    "plot(xplot,relu.(xplot))\n",
    "plot(xplot,sigmoid.(xplot));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The loss functions defines how well of neural network reproduces the data\n",
    "* for a regression problem the loss is often the L2 norm, representing how close the prediction $\\mathbf y'$ are to the observations $\\mathbf y$:\n",
    "\n",
    "$$\n",
    "J(\\mathbf y') = || \\mathbf y - \\mathbf y' ||^2\n",
    "$$\n",
    "\n",
    "* if neural network predict probabilities, then it is common to use the negative log likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "δloss (generic function with 1 method)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss(y,yp) = sum(abs2,y - yp)/length(y)\n",
    "δloss(y,yp,δyp) = (sum((y - yp).^2 / length(y)), -2*δyp ⋅ (y - yp)/length(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((2, 1000), (20, 2))"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size(x), size(w[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: redefining constant funs\n",
      "WARNING: redefining constant ∇funs\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "15.343450361141437"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "layer(w,b,x) = w*x .+ b\n",
    "δlayer(w,b,x,δw,δb,δx) = (w*x .+ b, δb .+ (δw*x + w*δx))\n",
    "\n",
    "∇identity(x) = one(x)\n",
    "\n",
    "\n",
    "const funs = [sigmoid,sigmoid,identity]\n",
    "const ∇funs = [∇sigmoid,∇sigmoid,∇identity]\n",
    "\n",
    "\n",
    "\n",
    "function predict(w::Vector{TA},b,x) where TA\n",
    "    K = length(b)+1    \n",
    "    yp = Vector{TA}(undef,K)\n",
    "    \n",
    "    yp[1] = x    \n",
    "    for i = 1:K-1\n",
    "       yp[i+1] = funs[i].(layer(w[i],b[i],yp[i]))\n",
    "    end\n",
    "    \n",
    "    return yp[end]\n",
    "end\n",
    "\n",
    "function cost(w,b,x,y)    \n",
    "    yp = predict(w,b,x)\n",
    "    return loss(y,yp)\n",
    "end\n",
    "\n",
    "cost(w,b,x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.346847716995503"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eps = 1e-4\n",
    "\n",
    "δb = [eps*randn(size(tmp)) for tmp in b]\n",
    "δw = [eps*randn(size(tmp)) for tmp in w]\n",
    "\n",
    "b2 = [tmp + δtmp for (tmp,δtmp) in zip(b,δb)]\n",
    "w2 = [tmp + δtmp for (tmp,δtmp) in zip(w,δw)]\n",
    "\n",
    "J2 = cost(w2,b2,x,y) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.343450361141437"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost(w,b,x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "δc_diff = (cost(w2,b2,x,y) \n",
    "         - cost(w,b,x,y)) / eps\n",
    "\n",
    "function δpredict(w,b,x,δw,δb)\n",
    "    K = length(b)+1\n",
    "    \n",
    "    yp = copy(x)\n",
    "    δyp = zeros(size(x))\n",
    "    for i = 1:K-1\n",
    "       yp, δyp = δlayer(w[i],b[i],yp,δw[i],δb[i],δyp)\n",
    "       δyp = ∇funs[i].(yp) .* δyp\n",
    "       yp = funs[i].(yp) \n",
    "    end\n",
    "    \n",
    "    return yp,δyp \n",
    "end\n",
    "\n",
    "function δcost(w,b,x,y,δw,δb)\n",
    "    yp, δyp = δpredict(w,b,x,δw,δb)\n",
    "    return δloss(y,yp,δyp)\n",
    "end\n",
    "\n",
    "\n",
    "J,δJ =  δcost(w,b,x,y,δw,δb)\n",
    "\n",
    "@test δc_diff ≈ δJ/eps rtol=1e-2\n",
    "#@show δc_diff\n",
    "#@show δJ/eps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adjoint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "∂J = 1.\n",
    "\n",
    "t1 = ∂J * δcost(w,b,x,y,δw,δb)[2]\n",
    "\n",
    "function adj_loss(y,yp,∂J)\n",
    "    ∂yp = -2 * (y - yp) * ∂J / length(y)\n",
    "end\n",
    "\n",
    "\n",
    "function adj_layer(w,b,x,∂yp)\n",
    "    ∂b = sum(∂yp,dims=2)[:,1]\n",
    "    ∂w = (∂yp) * x'\n",
    "    ∂x = w' * ∂yp    \n",
    "    return ∂w,∂b,∂x\n",
    "end\n",
    "\n",
    "\n",
    "function adj_cost(w::Vector{Matrix{T}},b::Vector{Vector{T}},x,y,δJ) where T\n",
    "    N = length(b)\n",
    "    yp = Vector{Matrix{T}}(undef,N+1)\n",
    "    ∂yp = Vector{Matrix{T}}(undef,N+1)\n",
    "    ∂w = Vector{Matrix{T}}(undef,N)\n",
    "    ∂b = Vector{Vector{T}}(undef,N)\n",
    "    \n",
    "    # prediction - foreward\n",
    "    yp[1] = x\n",
    "    for i = 1:N\n",
    "      yp[i+1] = funs[i].(layer(w[i],b[i],yp[i]))\n",
    "    end\n",
    "    \n",
    "    # back-propagation\n",
    "    # now everything in reverse\n",
    "    ∂yp[N+1] = adj_loss(y,yp[N+1],∂J)\n",
    "    \n",
    "    for i = N:-1:1\n",
    "       ∇act = ∇funs[i].(w[i]*yp[i] .+ b[i])\n",
    "       ∂yp[i+1] = ∇act .* ∂yp[i+1]\n",
    "       ∂w[i],∂b[i],∂yp[i] = adj_layer(w[i],b[i],yp[i],∂yp[i+1])\n",
    "    end\n",
    "    \n",
    "    return ∂w,∂b\n",
    "end\n",
    "\n",
    "\n",
    "∂w,∂b = adj_cost(w,b,x,y,∂J)\n",
    "\n",
    "t2 = 0.\n",
    "for i = 1:length(b)\n",
    "    t2 = t2 + ∂w[i] ⋅ δw[i] + ∂b[i] ⋅ δb[i]\n",
    "end\n",
    "\n",
    "@test t1  ≈ t2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gradient descent\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cost(w, b, x, y) = 15.343450361141437\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "15.343450361141437"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@show cost(w,b,x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cost(w, b, x, y) = 15.343450361141437\n",
      "cost(w, b, x, y) = 19.52054721886225\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "19.52054721886225"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@show cost(w,b,x,y)\n",
    "\n",
    "η = 0.2 # learning rate\n",
    "\n",
    "# compute the gradient\n",
    "∂w,∂b = adj_cost(w,b,x,y,1.)\n",
    "\n",
    "# update weights and biases\n",
    "for i = 1:length(w)\n",
    "    w[i] = w[i] - η * ∂w[i]\n",
    "    b[i] = b[i] - η * ∂b[i]\n",
    "end\n",
    "@show cost(w,b,x,y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50-element Array{Int64,1}:\n",
       " 971\n",
       " 423\n",
       " 737\n",
       " 861\n",
       " 138\n",
       " 949\n",
       " 391\n",
       " 585\n",
       " 693\n",
       " 678\n",
       " 286\n",
       " 884\n",
       " 233\n",
       "   ⋮\n",
       " 160\n",
       " 742\n",
       " 968\n",
       " 504\n",
       " 589\n",
       " 673\n",
       " 990\n",
       "  65\n",
       " 258\n",
       "  22\n",
       " 674\n",
       "  10"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "batchsize = 50\n",
    "ibatch = randperm(N)[1:batchsize]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cost(w, b, x, y) = 19.52054721886225\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.08580510715793802"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@show cost(w,b,x,y)\n",
    "Niter = 1000\n",
    "η = 0.2 # learning rate\n",
    "C = zeros(Niter+1)\n",
    "\n",
    "\n",
    "for k = 1:Niter\n",
    "    C[k] = cost(w,b,x,y)\n",
    "    \n",
    "    # compute the gradient\n",
    "    ∂w,∂b = adj_cost(w,b,x,y,1.)\n",
    "    \n",
    "    # update weights and biases\n",
    "    for i = 1:length(w)\n",
    "      w[i] = w[i] - η * ∂w[i]\n",
    "      b[i] = b[i] - η * ∂b[i]\n",
    "    end  \n",
    "end\n",
    "C[Niter+1] = cost(w,b,x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(C);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cost(w, b, x, y) = 8.515619999594653\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.06575790875890493"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w,b = randnomwb(nneurons)\n",
    "\n",
    "@show cost(w,b,x,y)\n",
    "Niter = 1000\n",
    "η = 0.2 # learning rate\n",
    "C = zeros(Niter+1)\n",
    "\n",
    "\n",
    "for k = 1:Niter\n",
    "    C[k] = cost(w,b,x,y)\n",
    "    \n",
    "    \n",
    "    ibatch = randperm(N)[1:batchsize]\n",
    "    \n",
    "    # compute the gradient\n",
    "    ∂w,∂b = adj_cost(w,b,x[:,ibatch],y[:,ibatch],1.)\n",
    "    \n",
    "    # update weights and biases\n",
    "    for i = 1:length(w)\n",
    "      w[i] = w[i] - η * ∂w[i]\n",
    "      b[i] = b[i] - η * ∂b[i]\n",
    "    end  \n",
    "end\n",
    "C[Niter+1] = cost(w,b,x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(C);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×1000 Array{Float64,2}:\n",
       " 3.4285     2.66111   -0.75847  0.689855  …  1.2734       2.67232  3.01476 \n",
       " 0.282408  -0.928666   2.45713  2.15448      0.00950419  -1.38189  0.429473"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(w,b,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×1000 Array{Float64,2}:\n",
       " 2.98759    3.01582  -0.687498  0.583367  …  1.0595      2.31916  2.60557\n",
       " 0.385506  -1.04845   2.71239   2.00719      0.0807524  -1.19397  0.50745"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Float64,1}:\n",
       " -3.0"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i=1;j=1\n",
    "[gx[i,j]; gy[i,j]][2,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 1000)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Figure(PyObject <Figure size 1500x700 with 2 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf2 = zeros(size(gx))\n",
    "for j = 1:size(gx,2)\n",
    "   for i = 1:size(gx,1)\n",
    "        gf2[i,j] = predict(w,b,reshape([gx[i,j]; gy[i,j]],(2,1)))[1]\n",
    "    end\n",
    "end\n",
    "\n",
    "fig = figure(figsize=(15,7))\n",
    "subplot(1,2,1)\n",
    "pcolor(gx,gy,gf)\n",
    "title(\"Original function\")\n",
    "\n",
    "subplot(1,2,2)\n",
    "pcolor(gx,gy,gf2);\n",
    "title(\"Reconstructed function\");\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can we avoid to write gradient and ajoint of your neural network by-hand?\n",
    "* yes we can using e.g. ReverseDiff\n",
    "* However, we cannot use a vector of vectors (`b`) and vectors of matrices (`w`).\n",
    "* We have to pack (or `flatten`), all these quantities into a long vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Pkg.add(\"ReverseDiff\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "packwb (generic function with 1 method)"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "packwb(w,b) = cat(b..., collect.(Iterators.flatten.(w))..., dims = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "522-element Array{Float64,1}:\n",
       " -2.1325760929355866 \n",
       " -1.1958164058326237 \n",
       "  0.24274128454445543\n",
       " -1.282327967690409  \n",
       "  0.20455522103095716\n",
       "  0.12990464719157202\n",
       "  0.42278257353783283\n",
       " -0.41745565711036964\n",
       " -1.8897201498322598 \n",
       "  0.87373279533212   \n",
       "  1.6679857488321996 \n",
       "  0.5791231012996113 \n",
       " -1.9402706427632253 \n",
       "  ⋮                  \n",
       "  0.8142557269634012 \n",
       " -0.8341242780385133 \n",
       "  0.05328870196028632\n",
       " -1.5666261647516866 \n",
       "  1.8007947582383528 \n",
       " -0.3745227615910526 \n",
       " -1.9046138007778808 \n",
       " -0.4945576203423711 \n",
       "  0.16638461228575502\n",
       "  1.206312259422111  \n",
       " -0.2498859205560419 \n",
       "  0.39838711757257556"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wb = packwb(w,b)\n",
    "size.(b)\n",
    "wb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we need to provide the inverse function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "unpackwb (generic function with 1 method)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function unpackwb(wb::TA,nneurons) where TA\n",
    "    b = TA[]\n",
    "    w = []\n",
    "    j = 0\n",
    "    for i = 1:length(nneurons)-1\n",
    "        push!(b,wb[j+1:j+nneurons[i+1]])\n",
    "        j += +nneurons[i+1]\n",
    "    end\n",
    "    for i = 1:length(nneurons)-1\n",
    "        push!(w,reshape(wb[j+1:j + nneurons[i+1] * nneurons[i]],(nneurons[i+1],nneurons[i])))\n",
    "        j += +nneurons[i] * nneurons[i+1]\n",
    "    end\n",
    "    \n",
    "    return w,b\n",
    "end\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Packing and unpacking should return the original data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "  \n",
    "w2, b2 = unpackwb(wb,nneurons)\n",
    "@test b2 == b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@test w2 == w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Int64,1}:\n",
       "  2\n",
       " 20\n",
       " 20\n",
       "  2"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nneurons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Tuple{Int64,Int64},1}:\n",
       " (20, 2) \n",
       " (20, 20)\n",
       " (2, 20) "
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size.(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "using ReverseDiff: GradientTape, GradientConfig, gradient, gradient!, compile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: redefining constant f_tape\n",
      "WARNING: redefining constant compiled_f_tape\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "([-0.0019546802812835337, 0.004007889109976015, 0.0004962882872508583, -3.206784936308708e-5, 0.0053392703079379, -0.0030539278127217945, 0.0015895596802961182, -0.008036916368024852, -0.014922302681286227, 0.00945268200138327  …  0.020627322279839554, -0.013286777907751731, 0.0006192393509392364, -0.0002954269490382254, 0.010187177502658134, -0.005115888938878179, 0.011754079657286965, -0.012282894995802459, -0.00021194482028641837, 0.00018126008803330036],)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function costwb(wb)\n",
    "    w,b = unpackwb(wb,nneurons)\n",
    "    return cost(w,b,x,y)\n",
    "end\n",
    "\n",
    "const f_tape = GradientTape(costwb, (wb,))\n",
    "const compiled_f_tape = compile(f_tape)\n",
    "#extrema(results)\n",
    "\n",
    "function adj_cost2(w,b)\n",
    "    wb = packwb(w,b)\n",
    "    results = (similar(wb),)\n",
    "    gradient!(results, compiled_f_tape, (wb,))\n",
    "    return unpackwb(results[1],nneurons)\n",
    "end\n",
    "#maximum(gradient(costwb,(wb,))[1])\n",
    "\n",
    "#results = gradient(costwb,(wb,))[1]\n",
    "\n",
    "grad = (similar(wb),)\n",
    "\n",
    "#f_tape2 = GradientTape(costwb, (wb,))\n",
    "gradient!(grad, compiled_f_tape, (wb,))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eps = 1e-5\n",
    "e = zeros(size(wb))\n",
    "e[1,1] = 1\n",
    "\n",
    "@test (costwb(wb+eps*e) - costwb(wb))/eps ≈ grad[1][1] rtol=1e-3\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rwb = randn(size(wb))\n",
    "\n",
    "@test (costwb(wb + eps*rwb) - costwb(wb - eps*rwb))/(2eps) ≈ sum(rwb .* grad[1]) rtol=1e-3\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "∂w,∂b = adj_cost(w,b,x,y,1.)\n",
    "∂w2,∂b2 = adj_cost2(w,b)\n",
    "\n",
    "@test ∂w ≈ ∂w2\n",
    "@test ∂b ≈ ∂b2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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