GitHub_collection_pykan/tutorials/Example_11_encouraing_linear.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "095b0666",
   "metadata": {},
   "source": [
    "# Example 11: Encouraging linearity\n",
    "\n",
    "In cases where we don't know how deep we should set KANs to be, one strategy is to try from small models, grudually making models wider/deeper until we find the minimal model that performs the task quite well. Another strategy is to start from a big enough model and prune it down. This jupyter notebook demonstrates cases where we go for the second strategy. Besides sparsity along width, we also want activation functions to be linear ('shortcut' along depth)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef047a0f",
   "metadata": {},
   "source": [
    "There are two relevant tricks: \n",
    "\n",
    "(1) set the base function 'base_fun' to be linear; \n",
    "\n",
    "(2) penalize spline coefficients. When spline coefficients are zero, the activation function is linear."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91301ca0",
   "metadata": {},
   "source": [
    "### Case 1: 1D function \n",
    "\n",
    "$f(x)={\\rm sin}(\\pi x)$. Although we know a [1,1] KAN suffices, we suppose we don't know that and use a [1,1,1,1] KAN instead."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77f9e16d",
   "metadata": {},
   "source": [
    "without trick"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c881665b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "checkpoint directory created: ./model\n",
      "saving model version 0.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "| train_loss: 1.43e-03 | test_loss: 1.47e-03 | reg: 8.40e+00 | : 100%|█| 20/20 [00:03<00:00,  5.80it"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.1\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "from kan import *\n",
    "\n",
    "# create dataset f(x,y) = sin(pi*x). This task can be achieved by a [1,1] KAN\n",
    "f = lambda x: torch.sin(torch.pi*x[:,[0]])\n",
    "dataset = create_dataset(f, n_var=1)\n",
    "\n",
    "model = KAN(width=[1,1,1,1], grid=5, k=3, seed=0, noise_scale=0.1)\n",
    "\n",
    "model.fit(dataset, opt=\"LBFGS\", steps=20);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "201ceacf",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 500x600 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13c725a5",
   "metadata": {},
   "source": [
    "with tricks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a22ffff3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "checkpoint directory created: ./model\n",
      "saving model version 0.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "| train_loss: 5.23e-03 | test_loss: 4.93e-03 | reg: 1.19e+01 | : 100%|█| 20/20 [00:04<00:00,  4.68it"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.1\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "from kan import *\n",
    "\n",
    "# create dataset f(x,y) = sin(pi*x). This task can be achieved by a [1,1] KAN\n",
    "f = lambda x: torch.sin(torch.pi*x[:,[0]])\n",
    "dataset = create_dataset(f, n_var=1)\n",
    "\n",
    "# set base_fun to be linear\n",
    "model = KAN(width=[1,1,1,1], grid=5, k=3, seed=0, base_fun='identity', noise_scale=0.1)\n",
    "\n",
    "# penality spline coefficients\n",
    "model.fit(dataset, opt=\"LBFGS\", steps=20, lamb=1e-4, lamb_coef=10.0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c82c8db5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x600 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af370a4c",
   "metadata": {},
   "source": [
    "### Case 2: 2D function \n",
    "\n",
    "$f(x,y)={\\rm exp}({\\rm sin}(\\pi x)+y^2)$.  We know a [2,1,1] KAN represents it. Let's suppose we don't know about that and use a [2,3,3,3,1] KAN instead."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdba8357",
   "metadata": {},
   "source": [
    "without tricks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "5920bdaf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "checkpoint directory created: ./model\n",
      "saving model version 0.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "| train_loss: 3.11e-02 | test_loss: 3.13e-02 | reg: 3.66e+00 | : 100%|█| 50/50 [00:24<00:00,  2.07it"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.1\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# create dataset f(x,y) = exp(sin(pi*x)+y^2)\n",
    "f = lambda x: torch.exp(torch.sin(torch.pi*x[:,[0]]) + x[:,[1]]**2)\n",
    "dataset = create_dataset(f, n_var=2)\n",
    "\n",
    "model = KAN(width=[2,3,3,3,1], grid=3, k=3, noise_scale=0.5)\n",
    "model.fit(dataset, opt=\"LBFGS\", steps=50, lamb=0.01, reg_metric='edge_forward_spline_u');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "26af5d19",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x800 with 38 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "b0316bee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x800 with 14 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = model.prune(node_th=1e-1)\n",
    "model.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "9df646f2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rewind to model version 0.2, renamed as 1.2\n"
     ]
    }
   ],
   "source": [
    "model = model.rewind('0.2')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca1c5e86",
   "metadata": {},
   "source": [
    "with tricks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "1f82e8c0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "| train_loss: 5.05e-01 | test_loss: 5.94e-01 | reg: 4.57e+01 | : 100%|█| 20/20 [00:07<00:00,  2.75it"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 1.3\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "model.fit(dataset, opt=\"LBFGS\", steps=20, lamb=0.001, lamb_l1=0., lamb_entropy=0., lamb_coef=1.0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e09861b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x800 with 33 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e3c92b0d",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}