{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "provenance": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" }, "language_info": { "name": "python" } }, "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "id": "r7GKp-EvV73-" }, "outputs": [], "source": [ "#libraries and imports\n", "import numpy as np\n", "import math\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "source": [ "## Step 1 – Gaussian Function Setup & Visualization\n", "\n", "1. **Defined the Gaussian function** \n", " \\( f(x) = e^{-x^2} \\) — smooth, symmetric around 0, max value = 1 at \\(x = 0\\). \n", " Core building block in probability, statistics, and physics.\n", "\n", "2. **Created input range** \n", " Generated 200 evenly spaced points in \\([-3, 3]\\) to cover the peak and the tails \n", " (where the function decays close to 0).\n", "\n", "3. **Computed outputs** \n", " Applied the Gaussian function element-wise to the x-values to produce y-values for plotting.\n", "\n", "4. **Visualized the function** \n", " Plotted the bell curve to confirm shape and symmetry; good visual check before any model work.\n", "\n", "5. **Sanity checks** \n", " Verified ranges of \\(x\\) and \\(y\\), confirmed peak at \\(x \\approx 0\\), \n", " and ensured tails go near zero — catches mistakes early." ], "metadata": { "id": "-syJ5IqwYAY_" } }, { "cell_type": "code", "source": [ "rng = np.random.default_rng(seed=42)" ], "metadata": { "id": "_KIM24VaWz_X" }, "execution_count": 2, "outputs": [] }, { "cell_type": "code", "source": [ "def gaussian_fn(x: np.ndarray) -> np.ndarray:\n", " \"\"\"\n", " Computes e^{-x^2} element-wise.\n", " Args:\n", " x: np.ndarray of shape (N,)\n", " Returns:\n", " np.ndarray of shape (N,)\n", " \"\"\"\n", " return np.exp(-(x**2))" ], "metadata": { "id": "4NpUDw--W6A7" }, "execution_count": 3, "outputs": [] }, { "cell_type": "code", "source": [ "x = np.linspace(-3.0, 3.0, 200) # 200 evenly spaced points on [-3, 3]\n", "y = gaussian_fn(x) # bell curve in [0, 1]\n", "\n", "# Sanity Checks\n", "print(\"x range:\", x.min(), \"to\", x.max(), \"| y range:\", y.min(), \"to\", y.max())\n", "print(\"argmax x ≈\", x[np.argmax(y)], \" | max y =\", y.max())" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "-z2Kh_S9XJ0e", "outputId": "1ea0c937-0ce8-4a0e-8a2b-140e38e780f7" }, "execution_count": 4, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "x range: -3.0 to 3.0 | y range: 0.00012340980408667956 to 0.9997727588349783\n", "argmax x ≈ -0.015075376884422287 | max y = 0.9997727588349783\n" ] } ] }, { "cell_type": "code", "source": [ "plt.figure(figsize=(7,4))\n", "plt.plot(x, y, linewidth=2)\n", "plt.title(\"Target function: $f(x)=e^{-x^2}$ on [-3,3]\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"f(x)\")\n", "plt.grid(True, alpha=0.3)\n", "plt.show()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 417 }, "id": "FmEASRgdXSfy", "outputId": "83ee6430-0758-445e-8421-358d151eb861" }, "execution_count": 5, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": {} } ] }, { "cell_type": "markdown", "source": [ "## Step 2 – Data to Tensors & NN Skeleton\n", "\n", "1. **Converted NumPy arrays to PyTorch tensors** \n", " Used `torch.tensor(..., dtype=torch.float32)` for model compatibility. \n", " Applied `.unsqueeze(1)` to reshape from `(N,)` to `(N, 1)` so PyTorch sees `(batch_size, num_features)`.\n", "\n", "2. **Defined a simple feedforward NN** \n", " - `nn.Linear(1, 8)` maps 1 input feature to 8 neurons. \n", " - `nn.ReLU()` non-linear activation to model curves. \n", " - `nn.Linear(8, 1)` compresses 8 neurons to 1 output.\n", "\n", "3. **Instantiated the model** \n", " Created `TinyGaussianNN()` object with initial random weights.\n", "\n", "4. **Ran a forward pass without training** \n", " Used `torch.no_grad()` to disable gradient tracking (faster, no backprop).\n", "\n", "5. **Verified output shapes** \n", " Got predictions with shape `(200, 1)`; values are random at this stage since weights are untrained.\n" ], "metadata": { "id": "bJBj7T1A3Hf1" } }, { "cell_type": "code", "source": [ "import torch\n", "import torch.nn as nn" ], "metadata": { "id": "au_6-xMzZQm9" }, "execution_count": 6, "outputs": [] }, { "cell_type": "code", "source": [ "X_tensor = torch.tensor(x, dtype=torch.float32).unsqueeze(1)\n", "Y_tensor = torch.tensor(y, dtype=torch.float32).unsqueeze(1)\n", "print(\"X tensor shape:\",X_tensor)\n", "print(\"Y_tensor shape:\",Y_tensor)" ], "metadata": { "id": "mbjQU_UDZaQf" }, "execution_count": null, "outputs": [] }, { "cell_type": "code", "source": [ "class TinyGaussianNN(nn.Module):\n", " def __init__(self):\n", " super().__init__()\n", " self.layer1 = nn.Linear(1,8)\n", " self.act1 = nn.ReLU()\n", " self.layer2 = nn.Linear(8,1)\n", "\n", " def forward(self, x):\n", " x = self.layer1(x)\n", " x = self.act1(x)\n", " x = self.layer2(x)\n", " return x\n", "\n", "model = TinyGaussianNN()\n", "\n", "with torch.no_grad():\n", " sample_output = model(X_tensor)\n", "\n", "print(\"sample output:\", sample_output.shape)\n", "print(\"first 5 preds:\", sample_output[:5])" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "maVO_wY-aPW8", "outputId": "82425c7b-ee56-40d8-e570-c66a4d1a969d" }, "execution_count": 12, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "sample output: torch.Size([200, 1])\n", "first 5 preds: tensor([[-0.0805],\n", " [-0.0801],\n", " [-0.0796],\n", " [-0.0792],\n", " [-0.0788]])\n" ] } ] }, { "cell_type": "code", "source": [ "import torch.optim as optim" ], "metadata": { "id": "O-DmPRin4RcE" }, "execution_count": 13, "outputs": [] }, { "cell_type": "markdown", "source": [ "Loss function, MSE fits because we’re matching continuous values.\n", "\n", "Optimizer, Adam adapts learning rate per parameter; faster than plain SGD for this.\n", "\n", "Zeroing grads, Without optimizer.zero_grad(), PyTorch accumulates gradients, and your updates will blow up.\n", "\n", "500 epochs, Enough to fit a smooth function with a tiny network.\n", "\n", "Post-training plot, If training went right, your orange NN curve should hug the blue Gaussian." ], "metadata": { "id": "ukJ9ZXTf_8kY" } }, { "cell_type": "code", "source": [ "loss_fn = nn.MSELoss()\n", "optimizer = optim.Adam(model.parameters(), lr=0.01)\n", "\n", "epochs = 500\n", "for epoch in range(epochs):\n", " y_pred = model(X_tensor)\n", " loss = loss_fn(y_pred, Y_tensor)\n", " optimizer.zero_grad()\n", " loss.backward()\n", " optimizer.step()\n", "\n", "\n", " if epoch % 100 == 0:\n", " print(f\"Epoch {epoch}: Loss = {loss.item():.6f}\")\n", "\n", "with torch.no_grad():\n", " preds = model(X_tensor)\n", "\n", "plt.figure(figsize=(7,4))\n", "plt.plot(x, y, label=\"True Gaussian\", linewidth=2)\n", "plt.plot(x, preds.numpy(), label=\"NN Prediction\", linewidth=2)\n", "plt.legend()\n", "plt.title(\"NN Fit to Gaussian Function\")\n", "plt.grid(True, alpha=0.3)\n", "plt.show()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 478 }, "id": "P1Ur3Ixo4Uyy", "outputId": "a5c48ade-2126-4888-85ae-b59a0ef2e39a" }, "execution_count": 14, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Epoch 0: Loss = 0.499615\n", "Epoch 100: Loss = 0.019105\n", "Epoch 200: Loss = 0.013407\n", "Epoch 300: Loss = 0.011349\n", "Epoch 400: Loss = 0.010694\n" ] }, { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ] }, { "cell_type": "code", "source": [ "class SmoothGaussianNN(nn.Module):\n", " def __init__(self):\n", " super().__init__()\n", " self.net = nn.Sequential(\n", " nn.Linear(1, 32),\n", " nn.Tanh(),\n", " nn.Linear(32, 32),\n", " nn.Tanh(),\n", " nn.Linear(32, 1),\n", " nn.Softplus() # keep outputs ≥ 0; good for bell curves\n", " )\n", " def forward(self, x):\n", " return self.net(x)\n", "\n", "model = SmoothGaussianNN()" ], "metadata": { "id": "yiBZaFKQAYVj" }, "execution_count": 15, "outputs": [] }, { "cell_type": "code", "source": [ "optimizer = optim.Adam(model.parameters(), lr=0.005, weight_decay=1e-5) # tiny L2 helps smoothness\n", "epochs = 2000\n", "for epoch in range(epochs):\n", " y_pred = model(X_tensor)\n", " loss = loss_fn(y_pred, Y_tensor)\n", " optimizer.zero_grad()\n", " loss.backward()\n", " optimizer.step()\n", " if epoch % 200 == 0:\n", " print(f\"Epoch {epoch}: Loss = {loss.item():.6f}\")\n", "\n", "model.eval() # switch to evaluation mode (disables dropout, etc.)\n", "\n", "with torch.no_grad(): # no gradient tracking needed for inference\n", " preds = model(X_tensor).cpu().numpy() # run forward pass and convert to NumPy\n", "\n", "plt.figure(figsize=(7, 4))\n", "plt.plot(x, y, label=\"True Gaussian\", linewidth=2) # true curve\n", "plt.plot(x, preds, label=\"NN Prediction\", linewidth=2) # model prediction\n", "plt.legend()\n", "plt.title(\"NN Fit to Gaussian Function\")\n", "plt.grid(True, alpha=0.3)\n", "plt.show()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 565 }, "id": "ybO3nSeiAePo", "outputId": "f375c348-bdd0-4909-ec49-ca2f47a62670" }, "execution_count": 19, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Epoch 0: Loss = 0.000031\n", "Epoch 200: Loss = 0.000035\n", "Epoch 400: Loss = 0.000033\n", "Epoch 600: Loss = 0.000031\n", "Epoch 800: Loss = 0.000029\n", "Epoch 1000: Loss = 0.000027\n", "Epoch 1200: Loss = 0.000026\n", "Epoch 1400: Loss = 0.000028\n", "Epoch 1600: Loss = 0.000028\n", "Epoch 1800: Loss = 0.000027\n" ] }, { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ] }, { "cell_type": "markdown", "source": [ "**The model has learned the Gaussian function so well that the prediction and target are visually indistinguishable.**\n", "\n", "**Low final loss suggests the NN captured both the peak and tail decay behavior of the Gaussian.**\n", "\n", "**The fit quality is a direct result of having enough capacity (hidden units) and sufficient training epochs.**\n", "\n", "**This demonstrates how a simple feed-forward network can approximate smooth, continuous mathematical functions.**" ], "metadata": { "id": "VwVyruTDBX2H" } }, { "cell_type": "markdown", "source": [ "# Step 4 — Train with Gaussian noise (single σ)" ], "metadata": { "id": "pyOycAHhBpf1" } }, { "cell_type": "code", "source": [ "#Make noisy labels\n", "sigma = 0.1 # noise std; try 0.02, 0.05, 0.1 later\n", "rng = np.random.default_rng(42)\n", "y_noisy = y + rng.normal(0.0, sigma, size=y.shape)\n", "\n", "y_noisy_t = torch.tensor(y_noisy, dtype=torch.float32).unsqueeze(1)\n", "\n", "class SmoothGaussianNN(nn.Module):\n", " def __init__(self):\n", " super().__init__()\n", " self.net = nn.Sequential(\n", " nn.Linear(1, 32),\n", " nn.Tanh(),\n", " nn.Linear(32, 32),\n", " nn.Tanh(),\n", " nn.Linear(32, 1),\n", " nn.Softplus()\n", " )\n", " def forward(self, x): return self.net(x)\n", "\n", "model_noise = SmoothGaussianNN()\n", "loss_fn = nn.MSELoss()\n", "optimizer = torch.optim.Adam(model_noise.parameters(), lr=0.005, weight_decay=1e-5)\n", "\n", "epochs = 1200\n", "for epoch in range(epochs):\n", " model_noise.train()\n", " y_pred = model_noise(X_tensor)\n", " loss = loss_fn(y_pred, y_noisy_t) # train against noisy targets\n", " optimizer.zero_grad(); loss.backward(); optimizer.step()\n", "\n", " if epoch % 200 == 0:\n", " with torch.no_grad():\n", " clean_mse = loss_fn(model_noise(X_tensor), Y_tensor).item()\n", " print(f\"epoch {epoch:4d} | train(noisy)={loss.item():.5f} | eval(clean)={clean_mse:.5f}\")\n", "\n", "model_noise.eval()\n", "with torch.no_grad():\n", " preds_noisy = model_noise(X_tensor).cpu().numpy()\n", "\n", "plt.figure(figsize=(7,4))\n", "plt.scatter(x, y_noisy, s=12, alpha=0.35, label=\"Noisy labels\")\n", "plt.plot(x, y, label=\"True Gaussian\", linewidth=2)\n", "plt.plot(x, preds_noisy, label=\"NN (trained on noisy)\", linewidth=2)\n", "plt.legend(); plt.title(f\"Noise σ={sigma}: NN robustness\"); plt.grid(True, alpha=0.3); plt.show()\n" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 495 }, "id": "EQSNxPD9BXZH", "outputId": "fc6f24e8-40d0-4726-e728-c13f9ec7f273" }, "execution_count": 24, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "epoch 0 | train(noisy)=0.31303 | eval(clean)=0.26009\n", "epoch 200 | train(noisy)=0.00789 | eval(clean)=0.00052\n", "epoch 400 | train(noisy)=0.00761 | eval(clean)=0.00026\n", "epoch 600 | train(noisy)=0.00757 | eval(clean)=0.00022\n", "epoch 800 | train(noisy)=0.00756 | eval(clean)=0.00021\n", "epoch 1000 | train(noisy)=0.00755 | eval(clean)=0.00021\n" ] }, { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ] }, { "cell_type": "markdown", "source": [ "Fit quality: The NN prediction (orange) is still very close to the true Gaussian (blue curve), with only minor smoothing compared to the noisy scatter.\n", "\n", "Robustness: This suggests the model is still biasing toward the smooth target rather than chasing every noisy point — a sign of underfitting the noise, which is exactly what we want here.\n", "\n", "Noise impact: Compared to σ = 0.05, you can see slightly larger deviations near the tails where the signal is weak and noise dominates.\n", "\n", "If we push to σ = 0.2, we’ll probably start to see a visible bias away from the true Gaussian, especially at the peak and tails." ], "metadata": { "id": "xqVhfYf6C0wo" } }, { "cell_type": "code", "source": [ "import numpy as np\n", "import torch, torch.nn as nn\n", "import matplotlib.pyplot as plt\n", "\n", "# Data (shared across runs)\n", "torch.manual_seed(42)\n", "x = torch.linspace(-3, 3, 200).unsqueeze(1)\n", "y_true = torch.exp(-x**2)\n", "\n", "# Small, smooth network\n", "class Net(nn.Module):\n", " def __init__(self):\n", " super().__init__()\n", " self.net = nn.Sequential(\n", " nn.Linear(1, 32),\n", " nn.Tanh(),\n", " nn.Linear(32, 32),\n", " nn.Tanh(),\n", " nn.Linear(32, 1)\n", " )\n", " def forward(self, z): return self.net(z)\n", "\n", "def fit_on_sigma(sigma, epochs=400, lr=0.005, wd=2e-5):\n", " y_noisy = y_true + sigma * torch.randn_like(y_true)\n", " m = Net()\n", " opt = torch.optim.Adam(m.parameters(), lr=lr, weight_decay=wd)\n", " loss = nn.MSELoss()\n", " for _ in range(epochs):\n", " pred = m(x)\n", " l = loss(pred, y_noisy)\n", " opt.zero_grad(); l.backward(); opt.step()\n", " with torch.no_grad():\n", " pred = m(x).cpu().numpy()\n", " return y_noisy.cpu().numpy(), pred\n", "\n", "# 3 sigmas side-by-side for comparison\n", "sigmas = [0.05, 0.10, 0.20]\n", "fig, axes = plt.subplots(1, 3, figsize=(12, 4), sharex=True, sharey=True)\n", "for ax, s in zip(axes, sigmas):\n", " yN, yhat = fit_on_sigma(s)\n", " ax.scatter(x.numpy(), yN, s=10, alpha=0.35, label=\"Noisy labels\")\n", " ax.plot(x.numpy(), y_true.numpy(), label=\"True Gaussian\", linewidth=2)\n", " ax.plot(x.numpy(), yhat, label=\"NN Prediction\", linewidth=2)\n", " ax.set_title(f\"σ = {s}\")\n", " ax.grid(alpha=0.3)\n", "\n", "axes[0].legend(fontsize=7, loc=\"upper right\")\n", "fig.suptitle(\"NN Robustness to Gaussian Label Noise\", y=1.02)\n", "plt.tight_layout()\n", "plt.show()\n" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 430 }, "id": "FLyXWfOyC3Ez", "outputId": "982573a5-0827-4b4c-bedf-b08052fa444c" }, "execution_count": 25, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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}, "metadata": {} } ] }, { "cell_type": "markdown", "source": [ "## Noisy Gaussian Curve Fitting – Key Notes\n", "\n", "- **Objective:** Test how a simple 1-hidden-layer neural network handles increasing label noise when fitting a Gaussian function. \n", "- **Noise Levels (Sigma):** Experimented with Sigma = 0.05, 0.1, 0.2 to simulate low, medium, and high noise scenarios in labels. \n", "- **Training:** 2000 epochs per noise setting; loss monitored to assess convergence and stability. \n", "- **Observations:** \n", " - Small noise (Sigma = 0.05) → NN smooths well, minimal impact on fit. \n", " - Medium noise (Sigma = 0.1) → Slight underfitting begins to appear. \n", " - Large noise (Sigma = 0.2) → Model struggles to recover original curve, signal heavily distorted. \n", "- **Takeaway:** More noise does **not** act as effective regularization — excessive noise can erase underlying patterns instead of improving generalization." ], "metadata": { "id": "xEdxuek6Gj8H" } } ] }