notes.ipynb

{"cells":[{"cell_type":"markdown","metadata":{},"source":["# Neural Tangent Kernels\n","\n","A few notes on the theory behind NTKs, based on  \n","- [Belkin et al, 2018](https://arxiv.org/abs/1812.11118)\n","-  [Jacot et al, 2018](http://arxiv.org/abs/1806.07572)\n","- [Lee et al, 2018](https://arxiv.org/abs/1711.00165)\n","-  [Lee et al, 2019](http://arxiv.org/abs/1902.06720)  \n","- [Chizat et al,2019](https://papers.nips.cc/paper/8559-on-lazy-training-in-differentiable-programming.pdf)\n","\n"]},{"cell_type":"code","execution_count":3,"metadata":{},"outputs":[],"source":["import numpy as np \n","import matplotlib.pyplot as plt \n","from scipy.linalg import expm \n","from datetime import datetime"]},{"cell_type":"markdown","metadata":{},"source":["\n","## Background \n","\n","- unclear why and how neural networks generalise so well\n","- more or less impossible to understand learning dynamics in nonlinear network  \n","\n","### Bias/Variance Trade-Off in Neural networks (Belkin et al)\n","- bias/variance trade-off doesn't explain behaviour of neural networks:\n","- if increase size even beyound threshold required for convergence on training data, test error begins to drop again   \n","\n","![u-shaped loss](./belkin.jpg)  \n","\n","- authors introduce notion of double decent \n","- motivation for study of networks in inifinte width limit \n","\n","\n","### Infinite Width Neural Networks & Gaussian Processes  \n","In the infinite width limit, function specified by neural network can be understood as function drawn from a Gaussian Process.  \n","#### Background Reading:  \n","- Equivalence of infinite width random Nnets and GPs: [Neal, 1994a](https://www.cs.toronto.edu/~radford/ftp/pin.pdf)  \n","- Extension to Deep Nets: [Lee et al, 2018](https://arxiv.org/abs/1711.00165)    \n","- [my implementation of a Gaussian Process from scratch](https://github.com/TimoFlesch/NTK/blob/master/gaussian_process.ipynb)  \n","\n","Intuitive Explanation: Weights and biases are gaussian random variables. The sum of all inputs into a unit (i.e. its preactivations) is thus a sum of gaussian RVs which itself is a gaussian RV (CLT).     \n","\n","\n","#### Formally speaking\n","If $z_i = f_{i-1}(x_{i-1},\\theta)$ denotes the preactivations at layer $i$, then \n","$$\n","z_i \\sim \\mathcal{GP}(m(z(x)),K(z(x),z(x')))\n","$$\n"," as width goes to infinity.  \n","* Parameters have zero mean, i.e. \n","$$m(z) = \\mathbb{E}(z(x)) = 0$$\n","* Covariance matrix is given by kernel $$\\kappa(x,x') = \\langle z(x)z(x')\\rangle$$\n","* Can be extended to deep nets via induction  \n","\n","#### Interpretation\n","This is very cool from historical perspective: Nnets gained popularity in the 80s but computationally too demanding. Kernel methods took over. Now, nnets again on vogue. Good to know that there is a connection.\n","\n","#### Problem\n","This only holds for a randomly initialised network where only the readout layer is trained. Therefore, doesn't really help with understanding SGD training dynamics\n"]},{"cell_type":"markdown","metadata":{},"source":["\n","\n","## Neural Tangent Kernels \n","### *Neural Tangent Kernel (Jacot et al,2018)*  \n","#### Goal\n","   \n","We'd like to understand the learning dynamics of a neural network. Know great deal about dynamics in linear case (thanks Andrew!), but SGD in nonlinear network very hard to study.   \n","The NTK is a kernel for nnets trained end-to-end with SGD. It applies to networks in the infinite width limit (or more generally where the network is close to its linear approximation) Authors demonstrated that NTK at init is good approximation for time-varying NTK  and thus dynamics can be analytically described as long as network operates in kernel regime. \n","\n","#### Gradient Flows: Derivation of NTK\n","Let's have a look at training dynamics under Gradient Descent. Standard Formula:    \n","$$\n","\\theta_{t+1} = \\theta_{t} - \\eta \\nabla_\\theta L(\\theta_t) \n","$$\n","$$\n","\\frac{\\theta_{t+1}-\\theta{t}}{\\eta} = -\\nabla_\\theta L(\\theta_t)\n","$$\n","We assume an L2 loss:\n","$$\n","L(\\theta) = \\frac{1}{2}||y(\\theta,x)-\\hat{y}||\n","$$\n","If we assume an infinitesimally small learning rate $\\eta$, we can interpret this as differential equation that tracks the change of the parameter vectors over time (**Gradient Flow**):\n","$$ \n","\\frac{d\\theta(t)}{dt} = \\dot{\\theta} = -\\nabla_\\theta L(\\theta_t) \n","$$\n","$$\n"," \\dot{\\theta} = -\\nabla_\\theta y(\\theta)(y(\\theta)-\\hat{y})\n","$$\n","Now here comes the cool part: We're dealing with a neural network, so the chain rule of calculus applies! This means that we can derive the dynamics of the model outputs (i.e. dynamics in function space) induced by the dynamics of the weights very easily:\n","$$\n","\\dot{y(\\theta)} = \\nabla_\\theta y(\\theta)^T\\dot{\\theta} \n","$$\n","$$\n","= -\\nabla_\\theta y(\\theta)^T\\nabla_\\theta y(\\theta)(y(\\theta)-\\hat{y})\n","$$\n","Now, we assume that the gradient of the network function acts as a feature map $\\phi(x)$, which implies that its dot product over all the data points is a valid kernel, the Neural Tangent Kernel (NTK):\n","$$ \n","H(t) = \\kappa_{NTK}(x,x') =  \\langle -\\nabla_\\theta y(\\theta(t),x)^T\\nabla_\\theta y(\\theta(t),x) \\rangle, \\forall x,x' \\in \\mathbb{R}^d \n","$$\n","\n","#### Lazy Learning: NTK and the Infinite Width Limit\n","In the infinite width limit, we make an interesting observation: Weights change only very little during training, i.e. stay close to their random initialisation:\n","$$\n","\\frac{||\\theta(t)-\\theta(0)||_2}{||\\theta(0)||_2} \\approx 0\n","$$ \n","And hence, the kernel barely varies during training:\n","$$\n","\\kappa_t(x,x') \\approx \\kappa_{t}(x,x'), \\forall t \n","$$ \n","Let's come up with an intuitive explanation of this phenomenon: With infinitely many weights, very small changes lead to a big **net change** in the preactivations (i.e. linearity) of a hidden layer neuron. In contrast, with only very few weights, these have to change substantially to yield the same effect.  \n","Moreover, Jacot has shown that the kernel at initialisation, which depends on a random variable (weights drawn from iid gaussian) converges in probability to a deterministic value in the large weight limit, i.e. \n","$$\n","\\kappa_0(x,x') \\approx \\kappa_{NTK}(x,x')\n","$$\n","So now we know that the time-varying kernel is essentially identical to the NTK. Importantly, the network trained to convergence is equivalent to the kernel regression solution with an NTK\n","$$\n","f_{SGD}(x,\\theta) \\approx f_{NTK}(x,\\theta) = \\kappa_{NTK}(x,X)^T \\kappa_{NTK}(X,X)^{-1}y\n","$$\n","where $X$ corresponds to the dataset s.t. $\\kappa_{NTK}(x,X) = [\\kappa_{NTK}(x,x_1),...,\\kappa_{NTK}(x,x_n)]^T$\n","\n","\n","#### Linear Approximation of Infinite Width Network (Lee et al,2019)  \n","At this point, it's still not clear to me how to study the dynamics of the network. However, we know that - in the NTK regime - the network parameters barely change during learning. Insight: We can just apply a 1st-order Taylor expansion (hence a linear approximation) to the network function w.r.t. its parameters around its initialisation. Now, the non-linear network is a linear function of the weights, yet still non-linear in its inputs:\n","$$\n","f(x,\\theta) \\approx f(x,\\theta_0) + \\nabla_\\theta f(x,\\theta_0)^T(\\theta-\\theta_0)\n","$$\n","And here comes the connection to NTKs: We can understand this as a linear function of x with a non-linear basis function (feature map) of the inputs, which is simply the gradient on the weights:\n","$$\n","\\phi(x) = \\nabla_\\theta f(x,\\theta_0)\n","$$\n","so the function becomes: \n","$$\n","f(x,\\theta) \\approx f(x,\\theta_0) + \\phi(x)^T(\\theta-\\theta_0)\n","$$\n","This feature map can be understood as a kernel on the inputs, for which we know its form:\n","$$\n","\\kappa(x,x') = \\phi(x)^T\\phi(x') = \\nabla_\\theta f(x,\\theta_0)^T \\nabla_\\theta f(x,\\theta_0)\n","$$\n","\n","Now, the training dynamics are tractable, as we have a linear function of the weights.\n","\n","\n","#### Analytic Solution to the training dynamics \n","So far, I have understood that the training dynamics can be described by a gradient flow. The expression for this contains the NTK. However, the NTK itself is still dependent on t, i.e. a time-varying process. From the theory of infinite width networks, we known that weights of infinitely wide networks barely change during training (see my intuitive explanation above) and that the network can be approximated by its linearisation. Hence, when in the kernel regime (i.e. barely changing Jacobian, i.e. close to its linearisation) the time-varying kernel of the neural network can be approximated by the kernel at initialisation \n","$$\n","\\nabla y(\\theta(t)) \\approx \\nabla y(\\theta_0)\n","$$ \n","$$\n","H(\\theta(t)) \\approx H(\\theta_0)\n","$$\n","\n","This is very good news, as we can update our expression for the gradient flow, which used to be:\n","$$\n","\\dot{y(\\theta)} = \\nabla_\\theta y(\\theta)^T\\dot{\\theta} = H(\\theta(t)) y(\\theta)-\\hat{y})\n","$$\n","Now, it becomes  \n","$$\n","\\dot{y(\\theta)} = \\nabla_\\theta y(\\theta)^T\\dot{\\theta} = H(\\theta_0) y(\\theta)-\\hat{y})\n","$$\n","**The equilibrium for this equation is achieved when the training loss is zero.**\n","Let's simplify this expression with a substitution of variables\n","$$ \n","u = y(\\theta)-\\hat{y}\n","$$ \n","Now the ODE becomes \n","$$ \n"," \\dot{u} = -H(\\theta_0)u \n","$$ \n","Ok, cool. A system of differential equations can be solved with the matrix exponential. So let's derive the output (recall: difference between output and predictions to be precise) at time t \n","$$ \n","y(\\theta(t))-\\hat{y} = u(t) = u(0)e^{-H(\\theta_0)t}\n","$$ \n","Awesome, we're now able to track the learning dynamics of a neural network using the NTK at initialisation! And we have shown that the SGD converges to zero training loss as long as the non-linear model is close to its linearisation (i.e. in the infinite weight limit)\n","\n"]},{"cell_type":"markdown","metadata":{},"source":["\n","## Lazy Learning and NTK Regime on standard Neural Networks (chizat et al, 2019)\n","\n","All above is pretty cool, but only holds in the infinite width limit. I understand intuitively why. With many weights, each contributes a little, thus ensemble has large impact on output, thus no need for dramatic changes (highly distributed code).\n","But in reality, width is obs. finite. How to apply these findings to real nnets?\n","**Chizat et al argue that a finite-width network can be pushed into the NTK regime by chosing an appropriate explicit scaling factor.**They demonstrate that any parametric model (not only nnets) can be trained in lazy regime if its outputs are close to zero after random initialisation. \n","If I understand correctly, this can be achieved with LeCun initialisation (variance scales with network width)"]},{"cell_type":"markdown","metadata":{},"source":["# A practical example\n","Let's consider a practical example. \n","We're going to use a simple MLP to solve the XOR-Problem and use an NTK to derive the learning dynamics. We'll investigate how initialisation schemes and network width determine whether or not the network operates in the kernel regime. But before we start, we need to define a few helper functions"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["from numpy.linalg import norm\n","# define a couple of helper functions\n","def relu(x):\n","    return x*(x>0)\n","def deriv_relu(x):\n","    return (x>0).astype('double')\n","\n","def loss(y_,y):\n","    return .5*norm(y_-y,2)**2\n","def deriv_loss(y_,y): \n","    return (y_-y)\n","\n","def compute_relchange(w0,wt):    \n","    return (norm(wt.flatten())-norm(w0.flatten()))/norm(w0.flatten())"]},{"cell_type":"markdown","metadata":{},"source":["## Problem Formulation\n","Given two binary variables, the network should return 1 if one of them is set to 1 and 0 otherwise.  \n","<table border='1px'>\n","<tr>\n","    <th>A </th>\n","    <th>B </th>\n","    <th>A xor B </th>\n","</tr>\n","<tr>\n","    <td> true </td>\n","    <td> true </td>\n","    <td> false </td>\n","</tr>\n","<tr>\n","    <td> false </td>\n","    <td> true </td>\n","    <td> true </td>\n","</tr>\n","<tr>\n","    <td> true </td>\n","    <td> false </td>\n","    <td> true </td>\n","</tr>\n","<tr>\n","    <td> false </td>\n","    <td> false </td>\n","    <td> false </td>\n","</tr>\n","\n","</table>"]},{"cell_type":"code","execution_count":4,"metadata":{},"outputs":[{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 Axes>","image/svg+xml":"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"263.63625pt\" version=\"1.1\" viewBox=\"0 0 386.845312 263.63625\" width=\"386.845312pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n <defs>\n  <style type=\"text/css\">\n*{stroke-linecap:butt;stroke-linejoin:round;}\n  </style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 263.63625 \nL 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\n"},"metadata":{"needs_background":"light"}}],"source":["# generate data \n","x = np.asarray([[1,1,-1,-1],[1,-1,1,-1]])\n","y = np.array([1,-1,-1,1])\n","plt.figure()\n","plt.scatter(x[0,:],x[1,:],c=y)\n","plt.title('XOR Problem')\n","y = y[np.newaxis,:]"]},{"cell_type":"markdown","metadata":{},"source":["\n","## SGD Solution\n","Let's first train a neural network with standard SGD. The network consists of an input layer (n=2), a hidden layer with relu nonlinearity (n=X) and an output layer (n=1). We'll use L2 loss on the network's predictions.   \n","### Network Architecture\n","\n","#### Dimensionalities\n","$$ \n","x \\in \\mathbb{R}^2, \n","h \\in \\mathbb{R}^n,  \n","y \\in \\mathbb{R}^1\n","$$ \n","\n","#### Forward Pass\n","$$ \n","h_{in} = xw_{hx} \\\\\n","h_{out} = max(0,h_{in}) \\\\\n","\\hat{y} = h_{out}w_{yh} \\\\\n","L = \\frac{1}{2}(\\hat{y}-y)^{2}\n","$$ \n","\n","#### Partial Derivatives\n","$$\n","\\frac{\\partial L}{\\partial \\hat{y}} = (\\hat{y}-y)\n","$$ \n","$$ \n","\\frac{\\partial \\hat{y}}{\\partial h_{out}} = w_{yh}\n","$$ \n","$$ \n","\\frac{\\partial \\hat{y}}{\\partial w_{yh}} = h_{out}\n","$$ \n","$$ \n","\\frac{\\partial h_{out}}{\\partial h_{in}} = \\mathbf{1}_{(h_{in}>0)} h_{in}\n","$$ \n","$$\n","\\frac{\\partial h_{in}}{\\partial x} = w_{hx}\n","$$\n","$$\n","\\frac{\\partial h_{in}}{\\partial w_{hx}} = x\n","$$\n","\n","#### Backward Pass \n","$$\n","\\Delta w_{yh} = \\nabla L_{w_{yh}} = \\frac{\\partial L}{\\partial \\hat{y}} \\frac{\\partial \\hat{y}}{\\partial w_{yh}}\n","$$\n","$$\n","\\Delta w_{yh} = (\\hat{y}-y)h_{out}\n","$$\n","$$ \n","\\Delta w_{hx} = \\nabla L_{w_{hx}} = \\frac{\\partial L}{\\partial \\hat{y}}  \\frac{\\partial \\hat{y}}{\\partial h_{out}} \\odot \\frac{\\partial h_{out}}{\\partial h_{in}}  \\frac{\\partial h_{in}}{\\partial w_{hx}}\n","$$\n","$$\n","\\Delta w_{hx} =  (\\hat{y}-y)w_{yh}\\odot (\\mathbf{1}_{(h_{in}>0)} h_{in}) x\n","$$ \n","\n","#### Weight Updates\n","\n","$$\n","w_{yh} = w_yh - \\eta\\Delta w_{yh}\n","$$\n","$$\n","w_{hx} = w_hx - \\eta\\Delta w_{hx}\n","$$"]},{"cell_type":"markdown","metadata":{},"source":[]},{"cell_type":"code","execution_count":5,"metadata":{},"outputs":[],"source":["# network trainer\n","def run_simulation(x,y,n_hidden=500,scale_w1=1/np.sqrt(2),scale_w2=1/500):\n","    #randomly initialise weights \n","    w_hx = scale_w1*np.random.randn(n_hidden,n_in)\n","    w_yh = scale_w2*np.random.randn(n_out,n_hidden)\n","    # store init weights\n","    w_hx_0 = w_hx \n","    w_yh_0 = w_yh\n","    w_relchange1 = []\n","    w_relchange2 = []\n","    losses = []\n","\n","\n","    # whole-dataset GD with several episodes\n","    for jj in range(n_iter):\n","        # forward pass \n","        h_in = w_hx.dot(x)\n","        h_out = relu(h_in)\n","        y_ = w_yh.dot(h_out)\n","        l = loss(y,y_)\n","        # partial derivatives\n","        dl_dy = deriv_loss(y_,y)\n","        dy_dh = w_yh \n","        dy_dw = h_out\n","        dho_dhi = deriv_relu(h_in)\n","        dhi_dw = x\n","        # backward pass:\n","        delta_dwyh = dl_dy.dot(dy_dw.T)\n","        delta_dwhx = (dl_dy.T.dot(dy_dh)*dho_dhi.T).T.dot(dhi_dw.T)\n","        \n","        # weight updates \n","        w_yh = w_yh - lrate*delta_dwyh \n","        w_hx = w_hx - lrate*delta_dwhx\n","\n","        # store relative weight change\n","        w_relchange1.append(compute_relchange(w_hx_0,w_hx))\n","        w_relchange2.append(compute_relchange(w_yh_0,w_yh))\n","        # store loss\n","        losses.append(l)\n","    return losses,w_relchange1,w_relchange2"]},{"cell_type":"markdown","metadata":{"tags":["outputPrepend"]},"source":["### Impact of Network Width on relative weight change during training"]},{"cell_type":"code","execution_count":6,"metadata":{"tags":[]},"outputs":[{"output_type":"stream","name":"stdout","text":"14/09/2020 12:03:58 - network 1/5\n14/09/2020 12:04:11 - network 2/5\n14/09/2020 12:04:24 - network 3/5\n14/09/2020 12:04:38 - network 4/5\n14/09/2020 12:04:53 - network 5/5\ndone\n"},{"output_type":"display_data","data":{"text/plain":"<Figure size 1120x400 with 3 Axes>","image/svg+xml":"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"352.23175pt\" version=\"1.1\" viewBox=\"0 0 1001.453125 352.23175\" width=\"1001.453125pt\" 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\n"},"metadata":{}}],"source":["# define network parameters \n","n_in = 2\n","n_out = 1\n","n_hidden_all = [5,10,50,500,2000]\n","n_runs = 20\n","n_iter = 5000\n","lrate = 1e-3\n","\n","# train network with sgd \n","all_losses = np.empty((len(n_hidden_all),n_runs,n_iter))\n","w_relchange1 = np.empty((len(n_hidden_all),n_runs,n_iter))\n","w_relchange2 = np.empty((len(n_hidden_all),n_runs,n_iter))\n","for ii, n in enumerate(n_hidden_all):\n","    print(datetime.now().strftime(\"%d/%m/%Y %H:%M:%S\") + ' - network ' + str(ii+1) + '/' + str(len(n_hidden_all)))\n","    for jj in range(n_runs):\n","        all_losses[ii,jj,:],w_relchange1[ii,jj,:],w_relchange2[ii,jj,:] = run_simulation(x,y,n_hidden=n,scale_w1=1/np.sqrt(2),scale_w2=1/n)\n","print(\"done\")\n","\n","\n","fig=plt.figure(figsize=(14, 5), dpi= 80, facecolor='w', edgecolor='k')\n","lines = []\n","for ii in range(len(n_hidden_all)):\n","    plt.subplot(1,3,1)\n","    plt.plot(np.mean(w_relchange1[ii,:,:],0))\n","    plt.title('relchange \\n w_in')\n","    plt.xlabel('iter')\n","    plt.ylabel('(||wt||-||w0||)/||w0||')\n","\n","    plt.subplot(1,3,2)\n","    plt.plot(np.mean(w_relchange2[ii,:,:],0))\n","    plt.title('relchange \\n w_out')\n","    plt.xlabel('iter')\n","    plt.ylabel('(||wt||-||w0||)/||w0||')\n","\n","    plt.subplot(1,3,3)\n","    line, = plt.plot(np.mean(all_losses[ii,:,:],0))\n","    lines.append(line)\n","    plt.title('loss')\n","    plt.xlabel('iter')\n","    plt.ylabel('loss')\n","    plt.tight_layout()\n","for ii in range(1,4):\n","    plt.subplot(1,3,ii)\n","    plt.legend(lines,n_hidden_all)"]},{"cell_type":"markdown","metadata":{},"source":["While the relative change of readout weights during training doesn't appear to depend heavily on the network width, we observe significant differences for the input weights. More specifically, unless the network has only very few hidden units, the input weights seem to stay very close to initialisation. Importantly, all networks were trained to convergence, indicating that even \"lazy\" networks are able to solve the task. "]},{"cell_type":"markdown","metadata":{},"source":["### Impact of scaling of initial weights on relative weight change during training (w_in only)\n","The previous findings made me wonder whether even very wide networks could be pushed out of the lazy training regime. To investigate this, I performed the same simulation but varied the magnitude by which the weights were scaled at initialisation. I expected that very small network weights would have to adapt substantially during training, whereas with large but randomly initialised weights, the net should operate in the kernel regime. The latter would make sense as any arbitrary mapping into a high-dimensional feature space should very likely be sufficient to solve a non-linear problem with a linear readout (see Cover's theorem)"]},{"cell_type":"code","execution_count":7,"metadata":{"tags":[]},"outputs":[{"output_type":"stream","name":"stdout","text":"14/09/2020 12:02:01 - network 1/4\n14/09/2020 12:02:16 - network 2/4\n14/09/2020 12:02:35 - network 3/4\n14/09/2020 12:02:57 - network 4/4\ndone\n"},{"output_type":"display_data","data":{"text/plain":"<Figure size 1120x400 with 3 Axes>","image/svg+xml":"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"352.23175pt\" version=\"1.1\" viewBox=\"0 0 1001.3625 352.23175\" width=\"1001.3625pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n 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define network parameters \n","n_in = 2\n","n_out = 1\n","n_hidden = 500\n","w1_init = [0.001,0.01,0.1,0.5]\n","w2_init = np.repeat(1/n_hidden,len(w1_init))\n","n_runs = 20\n","n_iter = 5000\n","lrate = 1e-3\n","\n","# train network with sgd \n","all_losses = np.empty((len(w1_init),n_runs,n_iter))\n","w_relchange1 = np.empty((len(w1_init),n_runs,n_iter))\n","w_relchange2 = np.empty((len(w1_init),n_runs,n_iter))\n","for ii, initval in enumerate(w1_init):\n","    print(datetime.now().strftime(\"%d/%m/%Y %H:%M:%S\") + ' - network ' + str(ii+1) + '/' + str(len(w1_init)))\n","    for jj in range(n_runs):\n","        all_losses[ii,jj,:],w_relchange1[ii,jj,:],w_relchange2[ii,jj,:] = run_simulation(x,y,n_hidden=n_hidden,scale_w1=initval,scale_w2=1/n_hidden)\n","print(\"done\")\n","\n","\n","fig=plt.figure(figsize=(14, 5), dpi= 80, facecolor='w', edgecolor='k')\n","lines = []\n","for ii in range(len(w1_init)):\n","    plt.subplot(1,3,1)\n","    plt.plot(np.mean(w_relchange1[ii,:,:],0))\n","    plt.title('relchange \\n w_in')\n","    plt.xlabel('iter')\n","    plt.ylabel('(||wt||-||w0||)/||w0||')\n","\n","    plt.subplot(1,3,2)\n","    plt.plot(np.mean(w_relchange2[ii,:,:],0))\n","    plt.title('relchange \\n w_out')\n","    plt.xlabel('iter')\n","    plt.ylabel('(||wt||-||w0||)/||w0||')\n","\n","    plt.subplot(1,3,3)\n","    line, = plt.plot(np.mean(all_losses[ii,:,:],0))\n","    lines.append(line)\n","    plt.title('loss')\n","    plt.xlabel('iter')\n","    plt.ylabel('loss')\n","    plt.tight_layout()\n","for ii in range(1,4):\n","    plt.subplot(1,3,ii)\n","    plt.legend(lines,w1_init)"]},{"cell_type":"markdown","metadata":{},"source":["As expected, all networks converged and were able to solve the XOR problem, but the relative change of network parameters depended heavily on the initial scaling of the input weights. Importantly, with very small intial input weights, both the input and readout weights changed substantially during training. In contrast, a large scaling factor ensured that the input weights remained close to intialisation (i.e. network operated in lazy learning regime), and so did the readout weights (even though to a mucm lesser extent)"]},{"cell_type":"markdown","metadata":{},"source":["## NTK Solution\n","Let's have a look at the learning dynamics derived from an NTK   \n","Remember that the NTK is defined as follows \n","$$ \n","H(t) = \\kappa_{NTK}(x,x') =  \\langle -\\nabla_\\theta y(\\theta(t),x)^T\\nabla_\\theta y(\\theta(t),x) \\rangle, \\forall x,x' \\in \\mathbb{R}^d \n","$$\n","Here, the gradient is applied to the *network function*, i.e. the whole neural network. \n","Let's jump straight to the implementation"]},{"cell_type":"markdown","metadata":{},"source":["### 1. Compute the NTK\n","we begin our NTK adventure by collecting the partial derivatives and setting up the gradient of the network function. We just need to stack the individual gradients - for input and readout weights - on top of each other.\n","As a reminder, these were the partial derivatives wrt the input and readout weights: \n","\n","$$\n","\\Delta w_{yh} = \\nabla L_{w_{yh}} = \\frac{\\partial L}{\\partial \\hat{y}} \\frac{\\partial \\hat{y}}{\\partial w_{yh}}\n","$$\n","$$\n","\\Delta w_{yh} = (\\hat{y}-y)h_{out}\n","$$\n","$$ \n","\\Delta w_{hx} = \\nabla L_{w_{hx}} = \\frac{\\partial L}{\\partial \\hat{y}}  \\frac{\\partial \\hat{y}}{\\partial h_{out}} \\odot \\frac{\\partial h_{out}}{\\partial h_{in}}  \\frac{\\partial h_{in}}{\\partial w_{hx}}\n","$$\n","$$\n","\\Delta w_{hx} =  (\\hat{y}-y)w_{yh}\\odot (\\mathbf{1}_{(h_{in}>0)} h_{in}) x\n","$$ "]},{"cell_type":"code","execution_count":9,"metadata":{},"outputs":[{"output_type":"execute_result","data":{"text/plain":"Text(0.5, 1.0, 'Neural Tangent Kernel')"},"metadata":{},"execution_count":9},{"output_type":"display_data","data":{"text/plain":"<Figure size 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define a few parameters \n","n_in = 2\n","n_hidden = 500\n","n_out = 1\n","scale_w1 = 0.5# 1/np.sqrt(2)\n","scale_w2 = 1/n_hidden \n","# init weights:\n","w_hx = scale_w1*np.random.randn(n_hidden,n_in)\n","w_yh = scale_w2*np.random.randn(n_out,n_hidden)\n","\n","# store init weights\n","w_hx_0 = w_hx \n","w_yh_0 = w_yh\n","\n","# cycle through datapoints and collect gradients\n","all_gradients = np.empty((n_hidden*(n_in+n_out),x.shape[1]))\n","for ii in range(x.shape[1]):\n","    xi = x[:,ii].reshape(2,1)\n","    yi = y[0][ii].reshape(1,1)\n","    \n","    # forward pass \n","    h_in = w_hx.dot(xi)\n","    h_out = relu(h_in)\n","    y_ = w_yh.dot(h_out)\n","    l = loss(yi,y_)\n","    # partial derivatives\n","    dl_dy = deriv_loss(y_,yi)\n","    dy_dh = w_yh \n","    dy_dw = h_out\n","    dho_dhi = deriv_relu(h_in)\n","    dhi_dw = xi\n","    # chain rule fun:\n","    dl_dwyh = dl_dy.dot(dy_dw.T)\n","    dl_dwhx = (dl_dy.T.dot(dy_dh)*dho_dhi.T).T.dot(dhi_dw.T)    \n","    # add to collection\n","    grad_vect = np.concatenate((dl_dwyh.flatten(),dl_dwhx.flatten()))\n","    all_gradients[:,ii] = grad_vect\n","# compute the NTK (dot product of gradients)\n","H = np.dot(all_gradients.T,all_gradients)\n","\n","# plot the ntk\n","plt.figure()\n","plt.imshow(H)\n","plt.title('Neural Tangent Kernel')"]},{"cell_type":"markdown","metadata":{},"source":["### 2. Derive network dynamics from NTK \n","\n","Remember that we can study the network dynamics with this NTK. For this, we only need to evaluate the NTK at initialisation (neat!) and solve the differential equation of the gradient flow for each time step: \n","$$ \n","y(\\theta(t))-\\hat{y} = u(t) = u(0)e^{-H(\\theta_0)t}\n","$$ \n"," "]},{"cell_type":"code","execution_count":11,"metadata":{"tags":[]},"outputs":[],"source":["# compute difference between labels and network output at initialisation\n","y_ = w_yh.dot(relu(w_hx.dot(x)))\n","u0 = y - y_\n","\n","# evaluate the loss for each time point\n","ts = np.linspace(0,0.5,num=500)\n","yh = np.empty((500,4))\n","l = np.empty((500))\n","for ii in range(ts.shape[0]):\n","    t = ts[ii]\n","    # matrix exponential used to compute solution to differential equation x(t) = x_0 * exp(t*A)\n","    u = np.dot(u0,expm(-H*t))    \n","    yh[ii,:] = y-u\n","    \n","    l[ii] = loss(y,yh[ii,:])\n","    "]},{"cell_type":"code","execution_count":13,"metadata":{"tags":[]},"outputs":[{"output_type":"stream","name":"stdout","text":"['w_scale= 0.001', 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\n"},"metadata":{"needs_background":"light"}}],"source":["# let's compare the loss derived from the NTK with the losses of the networks trained with SGD \n","w1_init = [0.001,0.01,0.1,0.5]\n","labels = ['w_scale= ' + str(ii) for ii in w1_init]\n","labels.append('NTK')\n","print(labels)\n","n_iter = 5000\n","lrate = 1e-3\n","tsgd = np.arange(0,n_iter)*lrate/10\n","plt.figure()\n","lines = []\n","for ii in range(all_losses.shape[0]):\n","    line, = plt.plot(tsgd,np.mean(all_losses[ii,:,:],0))\n","    lines.append(line)\n","    plt.title('loss')\n","    plt.xlabel('iter')\n","    plt.ylabel('loss')\n","    plt.tight_layout()\n","line, = plt.plot(ts,l,color='k')\n","lines.append(line)\n","plt.legend(lines,labels)"]},{"cell_type":"markdown","metadata":{},"source":["As expected, the NTK dynamics closely approximate the learning dynamics of a network with large weight initialisation"]}],"metadata":{"language_info":{"name":"python","codemirror_mode":{"name":"ipython","version":3},"version":"3.7.7-final"},"orig_nbformat":2,"file_extension":".py","mimetype":"text/x-python","name":"python","npconvert_exporter":"python","pygments_lexer":"ipython3","version":3,"kernelspec":{"name":"python37764bittf1conda04b2a24d8cc74909853187ab1e64d8db","display_name":"Python 3.7.7 64-bit ('tf1': conda)"}},"nbformat":4,"nbformat_minor":2}