What is Deep Learning?¶
Deep learning is a subset of machine learning that uses artificial neural networks to automatically learn patterns from large amounts of data. It is particularly useful for detecting complex relationships between inputs and outputs because it can model hierarchical and non-linear dependencies through multiple layers of neurons.
Tensorflow¶
An open-source deep learning framework developed by Google that provides tools for building, training, and deploying neural networks efficiently, often using GPUs or TPUs for acceleration.
Keras¶
A high-level API running on top of TensorFlow that simplifies building and training deep learning models with an intuitive and modular design.
Build a simple Neural Network¶
import tensorflow as tf # Importing the tensorflow library
import numpy as np # Importing numpy for numerical operations
Let's create our own data in order to understand the working structure of neural networks in a much better sense -
xs = np.array([-1.0, 0.0, 1.0, 2.0, 3.0, 4.0], dtype=float)
ys = np.array([-3.0, -1.0, 1.0, 3.0, 5.0, 7.0], dtype=float)
Now we will build the simplest model possible with one single layer and one single neuron. We will use Keras SEQUENTIAL class using which we can define network as a sequence of LAYERS. A single DENSE LAYER can be used to build the network.
model = tf.keras.models.Sequential([
tf.keras.Input(shape=(1,)), # This defines the input shape of the incoming data. This is not a layer
tf.keras.layers.Dense(units=1) # This is the first layer and has got 1 neuron defined by units=1
]
)
You have your model architecture build now, with 1 layer and 1 neuron. Now you have to compile the network and for this you need to specify two functions - loss and optimizer. For loss - we will use mean square error and for optimizer we will use stochastic gradient descent.
model.compile(optimizer='sgd', loss='mean_squared_error')
model.summary()
Model: "sequential"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━┩ │ dense (Dense) │ (None, 1) │ 2 │ └──────────────────────────────────────┴─────────────────────────────┴─────────────────┘
Total params: 2 (8.00 B)
Trainable params: 2 (8.00 B)
Non-trainable params: 0 (0.00 B)
The above gives the model summary that is the final model you have with you, using which you will start the training. Let's see what these three column means -
- Layer (type): indicates that the layer is a Dense (fully connected) layer. A Dense layer means that every neuron in the layer is connected to every neuron in the previous layer.
- Output Shape: (None, 1) -
- None: represents the batch size, which is unspecified at this point. The batch size will be determined when you input data into the model.
- 1: indicates that the layer has a single output unit (neuron).
- Param #: 2 - This is the total number of trainable parameters in the layer. In a Dense layer, the parameters include weights and biases.
- Weights: There is one weight for each connection between neurons in the previous layer and neurons in the current layer. If the previous layer has one neuron, there will be 1 weight.
- Bias: Each neuron in the Dense layer has one bias parameter.
- In this case, the layer has: 1 weight (from the single neuron in the previous layer to the single neuron in this layer). 1 bias. So 1+1=2 parameters.
Now is the time to train the model - where it learns the relationship between x and y and is done using the fit() method of the model object.
model.fit(xs, ys, epochs = 500)
#epochs means that it will loop for 500 times
Epoch 1/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 2s 2s/step - loss: 12.5066 Epoch 2/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 57ms/step - loss: 10.0657 Epoch 3/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 8.1406 Epoch 4/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 6.6215 Epoch 5/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 5.4219 Epoch 6/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 4.4738 Epoch 7/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 3.7235 Epoch 8/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 3.1291 Epoch 9/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 29ms/step - loss: 2.6573 Epoch 10/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 2.2821 Epoch 11/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 30ms/step - loss: 1.9830 Epoch 12/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 39ms/step - loss: 1.7438 Epoch 13/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 49ms/step - loss: 1.5519 Epoch 14/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 44ms/step - loss: 1.3972 Epoch 15/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 44ms/step - loss: 1.2718 Epoch 16/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 39ms/step - loss: 1.1697 Epoch 17/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 1.0858 Epoch 18/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 39ms/step - loss: 1.0165 Epoch 19/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.9586 Epoch 20/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.9098 Epoch 21/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.8681 Epoch 22/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.8323 Epoch 23/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step - loss: 0.8010 Epoch 24/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.7734 Epoch 25/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 46ms/step - loss: 0.7487 Epoch 26/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.7264 Epoch 27/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.7061 Epoch 28/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.6873 Epoch 29/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 38ms/step - loss: 0.6698 Epoch 30/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.6534 Epoch 31/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.6379 Epoch 32/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.6232 Epoch 33/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.6091 Epoch 34/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.5956 Epoch 35/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 38ms/step - loss: 0.5825 Epoch 36/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.5699 Epoch 37/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.5577 Epoch 38/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 27ms/step - loss: 0.5459 Epoch 39/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.5344 Epoch 40/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.5231 Epoch 41/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 46ms/step - loss: 0.5122 Epoch 42/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.5015 Epoch 43/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.4911 Epoch 44/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.4809 Epoch 45/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 38ms/step - loss: 0.4710 Epoch 46/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.4613 Epoch 47/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 38ms/step - loss: 0.4517 Epoch 48/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.4424 Epoch 49/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.4333 Epoch 50/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.4244 Epoch 51/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.4157 Epoch 52/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.4071 Epoch 53/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 53ms/step - loss: 0.3987 Epoch 54/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 51ms/step - loss: 0.3905 Epoch 55/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 48ms/step - loss: 0.3825 Epoch 56/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.3746 Epoch 57/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 28ms/step - loss: 0.3669 Epoch 58/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.3594 Epoch 59/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 27ms/step - loss: 0.3520 Epoch 60/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 25ms/step - loss: 0.3448 Epoch 61/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 27ms/step - loss: 0.3377 Epoch 62/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.3308 Epoch 63/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 37ms/step - loss: 0.3240 Epoch 64/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.3173 Epoch 65/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 31ms/step - loss: 0.3108 Epoch 66/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 31ms/step - loss: 0.3044 Epoch 67/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step - loss: 0.2982 Epoch 68/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.2920 Epoch 69/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 31ms/step - loss: 0.2860 Epoch 70/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.2802 Epoch 71/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step - loss: 0.2744 Epoch 72/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 46ms/step - loss: 0.2688 Epoch 73/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.2632 Epoch 74/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.2578 Epoch 75/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.2525 Epoch 76/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.2474 Epoch 77/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.2423 Epoch 78/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.2373 Epoch 79/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 29ms/step - loss: 0.2324 Epoch 80/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.2276 Epoch 81/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 46ms/step - loss: 0.2230 Epoch 82/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step - loss: 0.2184 Epoch 83/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.2139 Epoch 84/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 44ms/step - loss: 0.2095 Epoch 85/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.2052 Epoch 86/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step - loss: 0.2010 Epoch 87/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.1969 Epoch 88/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.1928 Epoch 89/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.1889 Epoch 90/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 66ms/step - loss: 0.1850 Epoch 91/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.1812 Epoch 92/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.1775 Epoch 93/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.1738 Epoch 94/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.1702 Epoch 95/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 127ms/step - loss: 0.1667 Epoch 96/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 47ms/step - loss: 0.1633 Epoch 97/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 47ms/step - loss: 0.1600 Epoch 98/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 53ms/step - loss: 0.1567 Epoch 99/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 49ms/step - loss: 0.1535 Epoch 100/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.1503 Epoch 101/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step - loss: 0.1472 Epoch 102/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 52ms/step - loss: 0.1442 Epoch 103/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 49ms/step - loss: 0.1412 Epoch 104/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 37ms/step - loss: 0.1383 Epoch 105/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 44ms/step - loss: 0.1355 Epoch 106/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.1327 Epoch 107/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 31ms/step - loss: 0.1300 Epoch 108/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 53ms/step - loss: 0.1273 Epoch 109/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 38ms/step - loss: 0.1247 Epoch 110/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 39ms/step - loss: 0.1221 Epoch 111/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.1196 Epoch 112/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.1172 Epoch 113/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.1148 Epoch 114/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 59ms/step - loss: 0.1124 Epoch 115/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 44ms/step - loss: 0.1101 Epoch 116/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 38ms/step - loss: 0.1078 Epoch 117/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 31ms/step - loss: 0.1056 Epoch 118/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 31ms/step - loss: 0.1035 Epoch 119/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.1013 Epoch 120/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 62ms/step - loss: 0.0992 Epoch 121/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 49ms/step - loss: 0.0972 Epoch 122/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 38ms/step - loss: 0.0952 Epoch 123/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0933 Epoch 124/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 37ms/step - loss: 0.0913 Epoch 125/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.0895 Epoch 126/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.0876 Epoch 127/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step - loss: 0.0858 Epoch 128/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.0841 Epoch 129/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0823 Epoch 130/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.0806 Epoch 131/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0790 Epoch 132/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.0774 Epoch 133/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 45ms/step - loss: 0.0758 Epoch 134/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 39ms/step - loss: 0.0742 Epoch 135/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 46ms/step - loss: 0.0727 Epoch 136/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0712 Epoch 137/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0697 Epoch 138/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step - loss: 0.0683 Epoch 139/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 49ms/step - loss: 0.0669 Epoch 140/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step - loss: 0.0655 Epoch 141/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 45ms/step - loss: 0.0642 Epoch 142/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 48ms/step - loss: 0.0629 Epoch 143/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 49ms/step - loss: 0.0616 Epoch 144/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.0603 Epoch 145/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.0591 Epoch 146/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 38ms/step - loss: 0.0579 Epoch 147/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 58ms/step - loss: 0.0567 Epoch 148/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 46ms/step - loss: 0.0555 Epoch 149/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0544 Epoch 150/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 30ms/step - loss: 0.0532 Epoch 151/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0522 Epoch 152/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 50ms/step - loss: 0.0511 Epoch 153/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0500 Epoch 154/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0490 Epoch 155/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0480 Epoch 156/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0470 Epoch 157/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 48ms/step - loss: 0.0460 Epoch 158/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 26ms/step - loss: 0.0451 Epoch 159/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 49ms/step - loss: 0.0442 Epoch 160/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0433 Epoch 161/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0424 Epoch 162/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.0415 Epoch 163/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.0407 Epoch 164/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.0398 Epoch 165/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0390 Epoch 166/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0382 Epoch 167/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0374 Epoch 168/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 49ms/step - loss: 0.0366 Epoch 169/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0359 Epoch 170/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.0352 Epoch 171/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0344 Epoch 172/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0337 Epoch 173/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 39ms/step - loss: 0.0330 Epoch 174/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 46ms/step - loss: 0.0324 Epoch 175/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 39ms/step - loss: 0.0317 Epoch 176/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 45ms/step - loss: 0.0310 Epoch 177/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0304 Epoch 178/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0298 Epoch 179/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0292 Epoch 180/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0286 Epoch 181/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0280 Epoch 182/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 37ms/step - loss: 0.0274 Epoch 183/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0268 Epoch 184/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 48ms/step - loss: 0.0263 Epoch 185/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 50ms/step - loss: 0.0258 Epoch 186/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 30ms/step - loss: 0.0252 Epoch 187/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0247 Epoch 188/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 49ms/step - loss: 0.0242 Epoch 189/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 49ms/step - loss: 0.0237 Epoch 190/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.0232 Epoch 191/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.0227 Epoch 192/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0223 Epoch 193/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step - loss: 0.0218 Epoch 194/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.0214 Epoch 195/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 37ms/step - loss: 0.0209 Epoch 196/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0205 Epoch 197/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 30ms/step - loss: 0.0201 Epoch 198/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 31ms/step - loss: 0.0197 Epoch 199/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 37ms/step - loss: 0.0193 Epoch 200/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0189 Epoch 201/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0185 Epoch 202/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 47ms/step - loss: 0.0181 Epoch 203/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0177 Epoch 204/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 25ms/step - loss: 0.0174 Epoch 205/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 31ms/step - loss: 0.0170 Epoch 206/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 26ms/step - loss: 0.0167 Epoch 207/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.0163 Epoch 208/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 30ms/step - loss: 0.0160 Epoch 209/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 25ms/step - loss: 0.0157 Epoch 210/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.0153 Epoch 211/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.0150 Epoch 212/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0147 Epoch 213/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 50ms/step - loss: 0.0144 Epoch 214/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 44ms/step - loss: 0.0141 Epoch 215/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.0138 Epoch 216/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0135 Epoch 217/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0133 Epoch 218/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 28ms/step - loss: 0.0130 Epoch 219/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0127 Epoch 220/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0125 Epoch 221/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 25ms/step - loss: 0.0122 Epoch 222/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 62ms/step - loss: 0.0119 Epoch 223/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step - loss: 0.0117 Epoch 224/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step - loss: 0.0115 Epoch 225/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.0112 Epoch 226/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.0110 Epoch 227/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 30ms/step - loss: 0.0108 Epoch 228/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 39ms/step - loss: 0.0106 Epoch 229/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 48ms/step - loss: 0.0103 Epoch 230/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0101 Epoch 231/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.0099 Epoch 232/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0097 Epoch 233/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.0095 Epoch 234/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 37ms/step - loss: 0.0093 Epoch 235/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 28ms/step - loss: 0.0091 Epoch 236/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 25ms/step - loss: 0.0089 Epoch 237/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0088 Epoch 238/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - loss: 0.0086 Epoch 239/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 27ms/step - loss: 0.0084 Epoch 240/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 48ms/step - loss: 0.0082 Epoch 241/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0081 Epoch 242/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.0079 Epoch 243/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.0077 Epoch 244/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 25ms/step - loss: 0.0076 Epoch 245/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.0074 Epoch 246/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 29ms/step - loss: 0.0073 Epoch 247/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 30ms/step - loss: 0.0071 Epoch 248/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.0070 Epoch 249/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.0068 Epoch 250/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 29ms/step - loss: 0.0067 Epoch 251/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 50ms/step - loss: 0.0065 Epoch 252/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.0064 Epoch 253/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0063 Epoch 254/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 50ms/step - loss: 0.0062 Epoch 255/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0060 Epoch 256/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0059 Epoch 257/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.0058 Epoch 258/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 30ms/step - loss: 0.0057 Epoch 259/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 28ms/step - loss: 0.0055 Epoch 260/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 25ms/step - loss: 0.0054 Epoch 261/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 52ms/step - loss: 0.0053 Epoch 262/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 46ms/step - loss: 0.0052 Epoch 263/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.0051 Epoch 264/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.0050 Epoch 265/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0049 Epoch 266/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 37ms/step - loss: 0.0048 Epoch 267/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 29ms/step - loss: 0.0047 Epoch 268/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0046 Epoch 269/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0045 Epoch 270/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 27ms/step - loss: 0.0044 Epoch 271/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 50ms/step - loss: 0.0043 Epoch 272/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0042 Epoch 273/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 25ms/step - loss: 0.0041 Epoch 274/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.0041 Epoch 275/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0040 Epoch 276/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 31ms/step - loss: 0.0039 Epoch 277/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.0038 Epoch 278/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0037 Epoch 279/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.0037 Epoch 280/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 29ms/step - loss: 0.0036 Epoch 281/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 28ms/step - loss: 0.0035 Epoch 282/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0034 Epoch 283/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 50ms/step - loss: 0.0034 Epoch 284/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0033 Epoch 285/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 0.0032 Epoch 286/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0032 Epoch 287/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 30ms/step - loss: 0.0031 Epoch 288/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 25ms/step - loss: 0.0030 Epoch 289/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 27ms/step - loss: 0.0030 Epoch 290/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 28ms/step - loss: 0.0029 Epoch 291/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 29ms/step - loss: 0.0029 Epoch 292/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.0028 Epoch 293/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 28ms/step - loss: 0.0027 Epoch 294/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step - loss: 0.0027 Epoch 295/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0026 Epoch 296/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0026 Epoch 297/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0025 Epoch 298/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 25ms/step - loss: 0.0025 Epoch 299/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.0024 Epoch 300/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 27ms/step - loss: 0.0024 Epoch 301/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.0023 Epoch 302/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.0023 Epoch 303/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.0022 Epoch 304/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 27ms/step - loss: 0.0022 Epoch 305/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 62ms/step - loss: 0.0021 Epoch 306/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0021 Epoch 307/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 26ms/step - loss: 0.0020 Epoch 308/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0020 Epoch 309/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 59ms/step - loss: 0.0020 Epoch 310/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.0019 Epoch 311/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 58ms/step - loss: 0.0019 Epoch 312/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0018 Epoch 313/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0018 Epoch 314/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 0.0018 Epoch 315/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 28ms/step - loss: 0.0017 Epoch 316/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 49ms/step - loss: 0.0017 Epoch 317/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 50ms/step - loss: 0.0017 Epoch 318/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0016 Epoch 319/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 27ms/step - loss: 0.0016 Epoch 320/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.0016 Epoch 321/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0015 Epoch 322/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 48ms/step - loss: 0.0015 Epoch 323/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 48ms/step - loss: 0.0015 Epoch 324/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 0.0014 Epoch 325/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 38ms/step - loss: 0.0014 Epoch 326/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.0014 Epoch 327/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.0014 Epoch 328/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 39ms/step - loss: 0.0013 Epoch 329/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 0.0013 Epoch 330/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 31ms/step - loss: 0.0013 Epoch 331/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 39ms/step - loss: 0.0012 Epoch 332/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0012 Epoch 333/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step - loss: 0.0012 Epoch 334/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.0012 Epoch 335/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0011 Epoch 336/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 0.0011 Epoch 337/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.0011 Epoch 338/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.0011 Epoch 339/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 0.0011 Epoch 340/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 0.0010 Epoch 341/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 0.0010 Epoch 342/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 28ms/step - loss: 9.9017e-04 Epoch 343/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 9.6983e-04 Epoch 344/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 51ms/step - loss: 9.4990e-04 Epoch 345/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step - loss: 9.3040e-04 Epoch 346/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 9.1129e-04 Epoch 347/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 8.9257e-04 Epoch 348/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 26ms/step - loss: 8.7423e-04 Epoch 349/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 25ms/step - loss: 8.5627e-04 Epoch 350/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 8.3868e-04 Epoch 351/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 8.2146e-04 Epoch 352/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 55ms/step - loss: 8.0458e-04 Epoch 353/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 44ms/step - loss: 7.8806e-04 Epoch 354/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 7.7187e-04 Epoch 355/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 48ms/step - loss: 7.5602e-04 Epoch 356/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 7.4048e-04 Epoch 357/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 7.2528e-04 Epoch 358/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 37ms/step - loss: 7.1038e-04 Epoch 359/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 6.9579e-04 Epoch 360/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 6.8149e-04 Epoch 361/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 6.6750e-04 Epoch 362/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 44ms/step - loss: 6.5379e-04 Epoch 363/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 48ms/step - loss: 6.4036e-04 Epoch 364/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 37ms/step - loss: 6.2721e-04 Epoch 365/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 6.1432e-04 Epoch 366/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 38ms/step - loss: 6.0170e-04 Epoch 367/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 5.8934e-04 Epoch 368/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 5.7724e-04 Epoch 369/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 5.6538e-04 Epoch 370/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 48ms/step - loss: 5.5377e-04 Epoch 371/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 5.4239e-04 Epoch 372/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 5.3125e-04 Epoch 373/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 47ms/step - loss: 5.2034e-04 Epoch 374/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 5.0965e-04 Epoch 375/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 48ms/step - loss: 4.9918e-04 Epoch 376/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 4.8893e-04 Epoch 377/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 4.7889e-04 Epoch 378/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 30ms/step - loss: 4.6905e-04 Epoch 379/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 4.5941e-04 Epoch 380/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 4.4998e-04 Epoch 381/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - 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loss: 1.7320e-04 Epoch 427/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 70ms/step - loss: 1.6965e-04 Epoch 428/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 46ms/step - loss: 1.6616e-04 Epoch 429/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 1.6275e-04 Epoch 430/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 1.5940e-04 Epoch 431/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 1.5613e-04 Epoch 432/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 1.5292e-04 Epoch 433/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 31ms/step - loss: 1.4978e-04 Epoch 434/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 30ms/step - loss: 1.4670e-04 Epoch 435/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 1.4369e-04 Epoch 436/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 56ms/step - loss: 1.4074e-04 Epoch 437/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 1.3785e-04 Epoch 438/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 1.3502e-04 Epoch 439/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 1.3224e-04 Epoch 440/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 1.2953e-04 Epoch 441/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 1.2687e-04 Epoch 442/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 1.2426e-04 Epoch 443/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 1.2171e-04 Epoch 444/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 30ms/step - loss: 1.1921e-04 Epoch 445/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 1.1676e-04 Epoch 446/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 1.1436e-04 Epoch 447/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 27ms/step - loss: 1.1201e-04 Epoch 448/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 25ms/step - loss: 1.0971e-04 Epoch 449/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 50ms/step - loss: 1.0746e-04 Epoch 450/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 38ms/step - loss: 1.0525e-04 Epoch 451/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 1.0309e-04 Epoch 452/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 1.0097e-04 Epoch 453/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 9.8897e-05 Epoch 454/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 30ms/step - loss: 9.6866e-05 Epoch 455/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 30ms/step - loss: 9.4876e-05 Epoch 456/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 29ms/step - loss: 9.2928e-05 Epoch 457/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 31ms/step - loss: 9.1018e-05 Epoch 458/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 8.9148e-05 Epoch 459/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 28ms/step - loss: 8.7318e-05 Epoch 460/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 36ms/step - loss: 8.5524e-05 Epoch 461/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 50ms/step - loss: 8.3768e-05 Epoch 462/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 8.2046e-05 Epoch 463/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 47ms/step - loss: 8.0361e-05 Epoch 464/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 7.8711e-05 Epoch 465/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 46ms/step - loss: 7.7094e-05 Epoch 466/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 7.5510e-05 Epoch 467/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 39ms/step - loss: 7.3958e-05 Epoch 468/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 7.2440e-05 Epoch 469/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 7.0951e-05 Epoch 470/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 6.9494e-05 Epoch 471/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 47ms/step - loss: 6.8067e-05 Epoch 472/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 37ms/step - loss: 6.6667e-05 Epoch 473/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 39ms/step - loss: 6.5299e-05 Epoch 474/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 6.3958e-05 Epoch 475/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 28ms/step - loss: 6.2643e-05 Epoch 476/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 6.1356e-05 Epoch 477/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 6.0096e-05 Epoch 478/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 5.8861e-05 Epoch 479/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 5.7653e-05 Epoch 480/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 5.6468e-05 Epoch 481/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 5.5309e-05 Epoch 482/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 39ms/step - loss: 5.4173e-05 Epoch 483/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 5.3061e-05 Epoch 484/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step - loss: 5.1970e-05 Epoch 485/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 39ms/step - loss: 5.0903e-05 Epoch 486/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 44ms/step - loss: 4.9857e-05 Epoch 487/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step - loss: 4.8833e-05 Epoch 488/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 4.7830e-05 Epoch 489/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 35ms/step - loss: 4.6847e-05 Epoch 490/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 4.5885e-05 Epoch 491/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 31ms/step - loss: 4.4942e-05 Epoch 492/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 37ms/step - loss: 4.4020e-05 Epoch 493/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 25ms/step - loss: 4.3116e-05 Epoch 494/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 82ms/step - loss: 4.2230e-05 Epoch 495/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 47ms/step - loss: 4.1363e-05 Epoch 496/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step - loss: 4.0513e-05 Epoch 497/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 33ms/step - loss: 3.9681e-05 Epoch 498/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step - loss: 3.8866e-05 Epoch 499/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 38ms/step - loss: 3.8068e-05 Epoch 500/500 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 31ms/step - loss: 3.7286e-05
<keras.src.callbacks.history.History at 0x1b32f8f1c30>
1/1 [==============================] - 0s 7ms/step - loss: 3.7374e-04 Epoch 408/500 1/1 [==============================] - 0s 10ms/step - loss: 3.6606e-04 Epoch 409/500 1/1 [==============================] - 0s 8ms/step - loss: 3.5855e-04 Epoch 410/500 1/1 [==============================] - 0s 11ms/step - loss: 3.5118e-04 Epoch 411/500 1/1 [==============================] - 0s 6ms/step - loss: 3.4397e-04 Epoch 412/500 1/1 [==============================] - 0s 8ms/step - loss: 3.3690e-04 Epoch 413/500 1/1 [==============================] - 0s 8ms/step - loss: 3.2998e-04 Epoch 414/500 1/1 [==============================] - 0s 8ms/step - loss: 3.2321e-04 Epoch 415/500 1/1 [==============================] - 0s 12ms/step - loss: 3.1656e-04 Epoch 416/500 1/1 [==============================] - 0s 9ms/step - loss: 3.1006e-04 Epoch 417/500 1/1 [==============================] - 0s 7ms/step - loss: 3.0370e-04 Epoch 418/500 1/1 [==============================] - 0s 9ms/step - loss: 2.9746e-04 Epoch 419/500 1/1 [==============================] - 0s 11ms/step - loss: 2.9135e-04 Epoch 420/500 1/1 [==============================] - 0s 8ms/step - loss: 2.8536e-04 Epoch 421/500 1/1 [==============================] - 0s 8ms/step - loss: 2.7950e-04 Epoch 422/500 1/1 [==============================] - 0s 13ms/step - loss: 2.7376e-04 Epoch 423/500 1/1 [==============================] - 0s 9ms/step - loss: 2.6813e-04 Epoch 424/500 1/1 [==============================] - 0s 11ms/step - loss: 2.6263e-04 Epoch 425/500 1/1 [==============================] - 0s 13ms/step - loss: 2.5723e-04 Epoch 426/500 1/1 [==============================] - 0s 13ms/step - loss: 2.5195e-04 Epoch 427/500 1/1 [==============================] - 0s 10ms/step - loss: 2.4677e-04 Epoch 428/500 1/1 [==============================] - 0s 10ms/step - loss: 2.4171e-04 Epoch 429/500 1/1 [==============================] - 0s 14ms/step - loss: 2.3674e-04 Epoch 430/500 1/1 [==============================] - 0s 11ms/step - loss: 2.3188e-04 Epoch 431/500 1/1 [==============================] - 0s 11ms/step - loss: 2.2712e-04 Epoch 432/500 1/1 [==============================] - 0s 9ms/step - loss: 2.2245e-04 Epoch 433/500 1/1 [==============================] - 0s 8ms/step - loss: 2.1788e-04 Epoch 434/500 1/1 [==============================] - 0s 7ms/step - loss: 2.1340e-04 Epoch 435/500 1/1 [==============================] - 0s 7ms/step - loss: 2.0902e-04 Epoch 436/500 1/1 [==============================] - 0s 10ms/step - loss: 2.0473e-04 Epoch 437/500 1/1 [==============================] - 0s 10ms/step - loss: 2.0052e-04 Epoch 438/500 1/1 [==============================] - 0s 8ms/step - loss: 1.9640e-04 Epoch 439/500 1/1 [==============================] - 0s 8ms/step - loss: 1.9237e-04 Epoch 440/500 1/1 [==============================] - 0s 10ms/step - loss: 1.8842e-04 Epoch 441/500 1/1 [==============================] - 0s 8ms/step - loss: 1.8455e-04 Epoch 442/500 1/1 [==============================] - 0s 8ms/step - loss: 1.8076e-04 Epoch 443/500 1/1 [==============================] - 0s 7ms/step - loss: 1.7704e-04 Epoch 444/500 1/1 [==============================] - 0s 9ms/step - loss: 1.7341e-04 Epoch 445/500 1/1 [==============================] - 0s 9ms/step - loss: 1.6984e-04 Epoch 446/500 1/1 [==============================] - 0s 8ms/step - loss: 1.6636e-04 Epoch 447/500 1/1 [==============================] - 0s 8ms/step - loss: 1.6294e-04 Epoch 448/500 1/1 [==============================] - 0s 8ms/step - loss: 1.5959e-04 Epoch 449/500 1/1 [==============================] - 0s 8ms/step - loss: 1.5632e-04 Epoch 450/500 1/1 [==============================] - 0s 8ms/step - loss: 1.5310e-04 Epoch 451/500 1/1 [==============================] - 0s 11ms/step - loss: 1.4996e-04 Epoch 452/500 1/1 [==============================] - 0s 9ms/step - loss: 1.4688e-04 Epoch 453/500 1/1 [==============================] - 0s 7ms/step - loss: 1.4386e-04 Epoch 454/500 1/1 [==============================] - 0s 7ms/step - loss: 1.4091e-04 Epoch 455/500 1/1 [==============================] - 0s 10ms/step - loss: 1.3801e-04 Epoch 456/500 1/1 [==============================] - 0s 8ms/step - loss: 1.3518e-04 Epoch 457/500 1/1 [==============================] - 0s 8ms/step - loss: 1.3240e-04 Epoch 458/500 1/1 [==============================] - 0s 8ms/step - loss: 1.2968e-04 Epoch 459/500 1/1 [==============================] - 0s 10ms/step - loss: 1.2702e-04 Epoch 460/500 1/1 [==============================] - 0s 8ms/step - loss: 1.2441e-04 Epoch 461/500 1/1 [==============================] - 0s 8ms/step - loss: 1.2185e-04 Epoch 462/500 1/1 [==============================] - 0s 11ms/step - loss: 1.1935e-04 Epoch 463/500 1/1 [==============================] - 0s 9ms/step - loss: 1.1690e-04 Epoch 464/500 1/1 [==============================] - 0s 7ms/step - loss: 1.1450e-04 Epoch 465/500 1/1 [==============================] - 0s 9ms/step - loss: 1.1214e-04 Epoch 466/500 1/1 [==============================] - 0s 12ms/step - loss: 1.0984e-04 Epoch 467/500 1/1 [==============================] - 0s 14ms/step - loss: 1.0759e-04 Epoch 468/500 1/1 [==============================] - 0s 12ms/step - loss: 1.0538e-04 Epoch 469/500 1/1 [==============================] - 0s 13ms/step - loss: 1.0321e-04 Epoch 470/500 1/1 [==============================] - 0s 11ms/step - loss: 1.0109e-04 Epoch 471/500 1/1 [==============================] - 0s 15ms/step - loss: 9.9013e-05 Epoch 472/500 1/1 [==============================] - 0s 11ms/step - loss: 9.6980e-05 Epoch 473/500 1/1 [==============================] - 0s 11ms/step - loss: 9.4989e-05 Epoch 474/500 1/1 [==============================] - 0s 11ms/step - loss: 9.3038e-05 Epoch 475/500 1/1 [==============================] - 0s 7ms/step - loss: 9.1127e-05 Epoch 476/500 1/1 [==============================] - 0s 7ms/step - loss: 8.9256e-05 Epoch 477/500 1/1 [==============================] - 0s 8ms/step - loss: 8.7422e-05 Epoch 478/500 1/1 [==============================] - 0s 8ms/step - loss: 8.5626e-05 Epoch 479/500 1/1 [==============================] - 0s 9ms/step - loss: 8.3867e-05 Epoch 480/500 1/1 [==============================] - 0s 7ms/step - loss: 8.2144e-05 Epoch 481/500 1/1 [==============================] - 0s 10ms/step - loss: 8.0458e-05 Epoch 482/500 1/1 [==============================] - 0s 7ms/step - loss: 7.8804e-05 Epoch 483/500 1/1 [==============================] - 0s 7ms/step - loss: 7.7186e-05 Epoch 484/500 1/1 [==============================] - 0s 10ms/step - loss: 7.5600e-05 Epoch 485/500 1/1 [==============================] - 0s 8ms/step - loss: 7.4046e-05 Epoch 486/500 1/1 [==============================] - 0s 8ms/step - loss: 7.2527e-05 Epoch 487/500 1/1 [==============================] - 0s 11ms/step - loss: 7.1037e-05 Epoch 488/500 1/1 [==============================] - 0s 7ms/step - loss: 6.9577e-05 Epoch 489/500 1/1 [==============================] - 0s 6ms/step - loss: 6.8147e-05 Epoch 490/500 1/1 [==============================] - 0s 9ms/step - loss: 6.6748e-05 Epoch 491/500 1/1 [==============================] - 0s 6ms/step - loss: 6.5378e-05 Epoch 492/500 1/1 [==============================] - 0s 12ms/step - loss: 6.4035e-05 Epoch 493/500 1/1 [==============================] - 0s 9ms/step - loss: 6.2719e-05 Epoch 494/500 1/1 [==============================] - 0s 10ms/step - loss: 6.1431e-05 Epoch 495/500 1/1 [==============================] - 0s 10ms/step - loss: 6.0169e-05 Epoch 496/500 1/1 [==============================] - 0s 10ms/step - loss: 5.8934e-05 Epoch 497/500 1/1 [==============================] - 0s 10ms/step - loss: 5.7723e-05 Epoch 498/500 1/1 [==============================] - 0s 13ms/step - loss: 5.6537e-05 Epoch 499/500 1/1 [==============================] - 0s 10ms/step - loss: 5.5376e-05 Epoch 500/500 1/1 [==============================] - 0s 7ms/step - loss: 5.4240e-05
<keras.callbacks.History at 0x146451fc6d0>
Now you have the model that has the knowledge of the relationship between xs and ys. Now we can use predict() method to predict for unknown xs values (that is unknown to the model)
new_x = np.array([12.0])
new_y = model.predict(new_x, verbose=0)
new_y
array([[22.977022]], dtype=float32)
new_y.item()
22.977022171020508
As per the numbers in xs and ys, it is showing the relationship of y=2x-1. However we got a little below 23 and not 23 exactly. This is because neural network deals with probabilities. So given the data that we fed to the model, it calculated that there is a very high probability that the relationship between x and y is y=2x-1, but with only 6 data points we cant be very much sure about this. As a result, for 12 we got value very close to 23 but not necessarily 23. Neural networks are data hungry models.
So what you did here?¶
- You generated your own data
- You created the model architecture with Input layer for the incoming data and 1 neural network layer with 1 neuron
- Compiled the model with loss and optimizer
- Fitted the model with training data
- Predicted on the trained model