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README.md

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+---
+license: mit
+tags:
+  - regression
+  - pytorch
+  - function-approximation
+  - single-hidden-layer
+---
+
+# ANN Approximation of y = x² — random_600_hidden6_mae_sigmoid
+
+A single-hidden-layer feedforward neural network trained to approximate
+**y = x²** on the interval **[-1, 1]**.
+
+## Model Details
+
+- **Architecture**: `Linear(1 → 6) → Sigmoid → Linear(6 → 1)`
+- **Hidden units**: 6
+- **Activation function**: sigmoid
+- **Loss function used in training**: mae
+- **Training dataset**: random sampling, 600 points, 80/20 train/val split
+- **Optimizer**: Adam, lr=0.01, full-batch gradient descent
+
+## Performance (validation set)
+
+| Metric | Value |
+|---|---|
+| MSE | 0.000006 |
+| RMSE | 0.002442 |
+| MAE | 0.001800 |
+| MAPE | 49.7565% |
+| R² | 0.9999 |
+
+This model was selected as the best-performing configuration out of a
+1350-run grid search sweeping dataset (10 variants), hidden-layer width
+(2–10), loss function (MSE/MAE/Huber), and activation function
+(ReLU/Tanh/Sigmoid/Leaky ReLU/ELU).
+
+## Usage
+
+```python
+import torch
+import torch.nn as nn
+
+class SingleHiddenLayerANN(nn.Module):
+    def __init__(self, hidden_units=6, activation="sigmoid"):
+        super().__init__()
+        self.hidden = nn.Linear(1, hidden_units)
+        self.output = nn.Linear(hidden_units, 1)
+        activations = {"relu": nn.ReLU(), "tanh": nn.Tanh(), "sigmoid": nn.Sigmoid(),
+                        "leaky_relu": nn.LeakyReLU(0.01), "elu": nn.ELU()}
+        self.activation = activations[activation]
+
+    def forward(self, x):
+        return self.output(self.activation(self.hidden(x)))
+
+model = SingleHiddenLayerANN()
+model.load_state_dict(torch.load("pytorch_model.bin", map_location="cpu"))
+model.eval()
+
+x = torch.tensor([[0.5]])
+y_pred = model(x)
+print(y_pred)  # should be close to 0.25 (0.5^2)
+```
+
+## Visualizing this model
+
+The `model.onnx` file in this repo can be opened directly at
+[netron.app](https://netron.app) (drag-and-drop, no install) to see the
+network graph, layer shapes, and weights interactively.
+
+## Source
+
+Full training pipeline, all 1350 experiment results, and analysis tools:
+see the linked GitHub repository.

config.json

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+{
+  "run_id": "random_600_hidden6_mae_sigmoid",
+  "sampling": "random",
+  "n_samples": 600,
+  "hidden_units": 6,
+  "loss": "mae",
+  "activation": "sigmoid",
+  "master_seed": 42,
+  "hyperparams": {
+    "optimizer": "adam",
+    "learning_rate": 0.01,
+    "epochs": 2000,
+    "batch_size": "full",
+    "checkpoint_every": 200,
+    "activation": "sigmoid"
+  },
+  "device": "cuda",
+  "resumed_from_checkpoint": false,
+  "training_seconds": 5.401285171508789,
+  "completed_at": "2026-07-21T19:35:45Z",
+  "software_versions": {
+    "python": "3.11.15",
+    "platform": "Windows-10-10.0.26200-SP0",
+    "torch": "2.11.0+cu128",
+    "numpy": "2.4.6",
+    "cuda_available": "True",
+    "cuda_version": "12.8",
+    "gpu_name": "NVIDIA GeForce RTX 4050 Laptop GPU"
+  },
+  "model_summary": "SingleHiddenLayerANN(hidden_units=6, activation=sigmoid)\n  Linear(1 -> 6)\n  Sigmoid()\n  Linear(6 -> 1)\n  Total trainable parameters: 19",
+  "metrics": {
+    "mse": 5.962054646594423e-06,
+    "rmse": 0.0024417318949046,
+    "mae": 0.0017995336077233,
+    "mape": 49.756466100269705,
+    "r2": 0.99993212811375
+  }
+}

model.onnx

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+version https://git-lfs.github.com/spec/v1
+oid sha256:fd4080b284b4e49bc2fdf1365a18422de871675f15e3fcdee1e9056e7c5c5203
+size 4479

pytorch_model.bin

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+version https://git-lfs.github.com/spec/v1
+oid sha256:6c7c55fd01e773c331d9b1eef6b7563bf252fcf48f8e92967f4a9d9a32935c16
+size 2585

weights.json

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+{
+  "architecture": {
+    "hidden_units": 6,
+    "activation": "sigmoid",
+    "layers": [
+      "Linear(1 -> h)",
+      "sigmoid()",
+      "Linear(h -> 1)"
+    ]
+  },
+  "hidden_layer": {
+    "weight": [
+      [
+        2.7088844776153564
+      ],
+      [
+        2.8541743755340576
+      ],
+      [
+        0.0023373549338430166
+      ],
+      [
+        1.5461868047714233
+      ],
+      [
+        0.0023936263751238585
+      ],
+      [
+        -2.2972044944763184
+      ]
+    ],
+    "bias": [
+      -2.926323890686035,
+      3.071049690246582,
+      0.8033617734909058,
+      -0.7763761878013611,
+      0.7987249493598938,
+      -2.333636999130249
+    ]
+  },
+  "output_layer": {
+    "weight": [
+      [
+        2.6142003536224365,
+        -1.274052619934082,
+        0.48730725049972534,
+        0.3808853030204773,
+        0.6062461137771606,
+        1.6951392889022827
+      ]
+    ],
+    "bias": [
+      0.062105655670166016
+    ]
+  },
+  "run_id": "random_600_hidden6_mae_sigmoid",
+  "metrics": {
+    "mse": 5.962054646594423e-06,
+    "rmse": 0.0024417318949046,
+    "mae": 0.0017995336077233,
+    "mape": 49.756466100269705,
+    "r2": 0.99993212811375
+  }
+}