{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# 2nd order optimization of neural nets using Gauss Newton\n", "\n", "In this notebook we will show to easily build 2nd order optimizers using cola." ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "First let's generate a suitable classification dataset.\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%load_ext autoreload\n", "%autoreload 2\n", "\n", "# Importing necessary libraries\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Function to generate the spiral dataset\n", "def generate_spiral_data(n_points, n_spirals, noise=0.02):\n", " X = np.zeros((n_points * n_spirals, 2))\n", " y = np.zeros(n_points * n_spirals, dtype=int)\n", " delta_theta = 4 * np.pi / n_spirals\n", " for i in range(n_spirals):\n", " theta = np.linspace(i * delta_theta, (i + 1) * delta_theta, n_points)\n", " r = np.linspace(0.0, 1, n_points)\n", " t = theta + np.random.randn(n_points) * noise\n", " X[i * n_points:(i + 1) * n_points] = np.column_stack((r * np.sin(t), r * np.cos(t)))\n", " y[i * n_points:(i + 1) * n_points] = i\n", " return X, y\n", "\n", "# Generating the spiral dataset with 100 points and 5 spirals\n", "n_points = 100\n", "n_spirals = 5\n", "X, y = generate_spiral_data(n_points, n_spirals)\n", "\n", "# Plotting the spiral dataset\n", "plt.scatter(X[:, 0], X[:, 1], c=y, cmap='jet', s=5)\n", "plt.title('Spiral Dataset')\n", "plt.xlabel('X1')\n", "plt.ylabel('X2')\n", "plt.xlim(-1, 1)\n", "plt.ylim(-1, 1)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import torch\n", "import torch.nn as nn\n", "import torch.optim as optim\n", "X = torch.tensor(X, dtype=torch.float32)\n", "y = torch.tensor(y, dtype=torch.long)\n", "def MLP(k=200):\n", " return nn.Sequential(\n", " nn.Linear(2, k), nn.SiLU(),\n", " nn.Linear(k, k), nn.SiLU(),\n", " nn.Linear(k, n_spirals))\n", " " ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "First lets train using 1000 epochs of SGD and Adam for comparison" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Epoch [100/500], Loss: 0.0317324697971344\n", "Epoch [200/500], Loss: 0.04851977527141571\n", "Epoch [300/500], Loss: 0.019817877560853958\n", "Epoch [400/500], Loss: 0.018510127440094948\n", "Epoch [500/500], Loss: 0.017751768231391907\n" ] } ], "source": [ "learning_rate = 1e-2\n", "epochs = 500\n", "\n", "model = MLP()\n", "criterion = nn.CrossEntropyLoss()\n", "optimizer = optim.Adam(model.parameters(), lr=learning_rate)\n", "adam_losses = []\n", "for epoch in range(epochs):\n", " # Forward pass\n", " outputs = model(X)\n", " loss = criterion(outputs, y)\n", "\n", " # Backward pass and optimization\n", " optimizer.zero_grad()\n", " loss.backward()\n", " optimizer.step()\n", "\n", " adam_losses.append(loss.item())\n", " if (epoch + 1) % 100 == 0:\n", " print(f'Epoch [{epoch + 1}/{epochs}], Loss: {loss.item()}')\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "Now lets make a 2nd order method using cola, here we will use the Gauss-Newton approximation to the Hessian as well the PSD Fisher matrix." ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "First let's make it so we can call as an explicit function of it's parameters (like in jax)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import torch.func as tf\n", "\n", "def flatten_params(params):\n", " shapes = [p.shape for p in params]\n", " flat_params = torch.cat([p.flatten() for p in params])\n", " return flat_params, shapes\n", "\n", "\n", "def unflatten_params(flat_params, shapes):\n", " params = []\n", " i = 0\n", " for shape in shapes:\n", " size = torch.prod(torch.tensor(shape)).item()\n", " param = flat_params[i:i + size]\n", " param = param.view(shape)\n", " params.append(param)\n", " i += size\n", " return params\n", "\n", "model = MLP()\n", "flat_p, shape = flatten_params(list(model.parameters()))\n", "flat_p = flat_p.detach().requires_grad_(True)\n", "\n", "def stateless_model(flatparams, x):\n", " params = unflatten_params(flatparams, shape)\n", " names = list(n for n, _ in model.named_parameters())\n", " nps = {n: p for n, p in zip(names, params)}\n", " return tf.functional_call(model, nps, x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's construct the Gauss Newton matrix to use as a PSD proxy for the Hessian in Newtons method.\n", "\n", "$G = \\sum_i J(x_i)^THJ(x_i)$ where $J\\in \\mathbb{R}^{C \\times p}$ is the Jacobian of the network for a single data point, $p$ is the number of parameters and $C$ is the number of outputs (classes).\n", "Here $H$ is the Hessian of the loss function with respect to the logits.\n", "\n", "Alternatively, we might consider Natural gradient descent (using the Fisher information matrix $F$).\n", "\n", "Here we will annotate the matrices as PSD so as to enable more efficient inversion methods, and we will add a small amount of Tikhonov regularization to the diagonal to improve the conditioning." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "import cola\n", "\n", "def flat_fn(p):\n", " return stateless_model(p, X).reshape(-1)\n", "\n", "def GN(p):\n", " \"\"\"Gauss-Newton approximation to the Hessian\"\"\"\n", " J = cola.ops.Jacobian(flat_fn, p)\n", " loss = lambda z: criterion(z.reshape(X.shape[0],-1),y)*n_spirals\n", " H = cola.ops.Hessian(loss, flat_fn(p))\n", " G = J.T @ H @ J\n", " return cola.PSD(G+1e-3*cola.ops.I_like(G))\n", "\n", "def Fisher(p):\n", " F = cola.ops.FIM(lambda p: stateless_model(p, X), p)\n", " return cola.PSD(F+1e-3*cola.ops.I_like(F))\n", "\n", "def flat_loss(params):\n", " return criterion(flat_fn(params).reshape(X.shape[0],-1), y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check the eigenvalues of GN and F to make sure they are not too big. Note that these matrices are already very big (40k x 40k), already far too large to use a dense method." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(41805, 41805)\n" ] } ], "source": [ "print(GN(flat_p).shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's check that the matrices are of a sensible scale via their largest eigenvalues:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "GN eigmax: 2.8789467811584473\n", "Fisher eigmax: 0.5777260065078735\n" ] } ], "source": [ "from cola import Auto\n", "with torch.no_grad():\n", " print(f\"GN eigmax: {cola.eigmax(GN(flat_p), alg=Auto(tol=1e-2))}\")\n", " print(f\"Fisher eigmax: {cola.eigmax(Fisher(flat_p), alg=Auto(tol=1e-2))}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we implement the optimization loop in this stateless manner.\n", "\n", "We limit the tolerance and max iterations of the (iterative) solves so as to reduce the computation time. Though we don't do so here, adding a preconditioner (e.g. Jacobi, PivotedCholesky, Nystrom) would substantially accelerate the convergence of the solves.\n", "Let's compare the two second order methods:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Epoch [10/500], Loss: 0.3142242431640625\n", "Epoch [20/500], Loss: 0.08766728639602661\n", "Epoch [30/500], Loss: 0.03646586090326309\n", "Epoch [40/500], Loss: 0.022148877382278442\n", "Epoch [50/500], Loss: 0.018077930435538292\n", "Epoch [60/500], Loss: 0.01689857430756092\n", "Epoch [70/500], Loss: 0.0165044367313385\n", "Epoch [80/500], Loss: 0.016341200098395348\n", "Epoch [90/500], Loss: 0.016260594129562378\n", "Epoch [100/500], Loss: 0.016215266659855843\n" ] } ], "source": [ "from cola import Auto, CG\n", "# Method 1: Hessian weighted Gauss Newton\n", "p = flat_p.clone()\n", "\n", "gnh_losses = []\n", "for epoch in range(epochs//5):\n", " with torch.no_grad(): # don't pay extra memory for recording the computation graph\n", " g = torch.func.grad(flat_loss)(p)\n", " p -= cola.inv(GN(p),alg=Auto(tol=1e-3, max_iters=20)) @ g\n", " loss = flat_loss(p)\n", " gnh_losses.append(loss.item())\n", " if (epoch+1) % 10 == 0:\n", " print(f'Epoch [{epoch + 1}/{epochs}], Loss: {loss.item()}')" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Epoch [10/500], Loss: 0.08653374761343002\n", "Epoch [20/500], Loss: 0.023038014769554138\n", "Epoch [30/500], Loss: 0.018084317445755005\n", "Epoch [40/500], Loss: 0.0170273520052433\n", "Epoch [50/500], Loss: 0.016643397510051727\n", "Epoch [60/500], Loss: 0.01646246947348118\n", "Epoch [70/500], Loss: 0.016362380236387253\n", "Epoch [80/500], Loss: 0.016300752758979797\n", "Epoch [90/500], Loss: 0.016259804368019104\n", "Epoch [100/500], Loss: 0.016231024637818336\n" ] } ], "source": [ "# Method 2: Natural gradient descent\n", "p = flat_p.clone()\n", "\n", "natural_gradient_losses = []\n", "for epoch in range(epochs//5):\n", " with torch.no_grad(): # don't pay extra memory for recording the computation graph\n", " g = torch.func.grad(flat_loss)(p)\n", " p -= .5*cola.inv(Fisher(p),alg=Auto(tol=1e-3, max_iters=20)) @ g\n", "\n", " loss = flat_loss(p)\n", " natural_gradient_losses.append(loss.item())\n", " if (epoch+1) % 10 == 0:\n", " print(f'Epoch [{epoch + 1}/{epochs}], Loss: {loss.item()}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Performing solves with these matrices for the 2nd order methods, we see that the optimization converges much faster per iteration than Adam." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(adam_losses, label='Adam', color='brown')\n", "plt.plot(natural_gradient_losses, label='Natural Gradient Descent', color='darkgreen')\n", "plt.plot(gnh_losses, label='Gauss-Newton Method', color='darkblue')\n", "\n", "plt.xlabel('iterations')\n", "plt.ylabel('loss')\n", "plt.yscale('log')\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_decision_boundary(model, X, y):\n", " # Creating a mesh grid\n", " x_min, x_max = X[:, 0].min() - 0.1, X[:, 0].max() + 0.1\n", " y_min, y_max = X[:, 1].min() - 0.1, X[:, 1].max() + 0.1\n", " h = 0.01\n", " xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n", " np.arange(y_min, y_max, h))\n", "\n", " # Predicting the class labels for the mesh grid\n", " Z = stateless_model(p, torch.tensor(np.c_[xx.ravel(), yy.ravel()], dtype=torch.float32))\n", " Z = torch.argmax(Z, axis=1)\n", " Z = Z.reshape(xx.shape)\n", "\n", " # Plotting the decision boundaries\n", " plt.contourf(xx, yy, Z.detach().numpy(), alpha=0.8, cmap='jet')\n", " plt.scatter(X[:, 0], X[:, 1], c=y, edgecolors='k', marker='o', s=50, linewidth=1, cmap='jet')\n", " plt.xlim(X[:, 0].min() - 0.1, X[:, 0].max() + 0.1)\n", " plt.ylim(X[:, 1].min() - 0.1, X[:, 1].max() + 0.1)\n", " plt.title('Decision Boundaries')\n", " plt.xlabel('X1')\n", " plt.ylabel('X2')\n", " plt.show()\n", "\n", "# Plotting the decision boundaries\n", "from functools import partial\n", "plot_decision_boundary(partial(stateless_model,p), X, y)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 4 }