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Path: blob/master/Applied Generative AI with GANS/3 Introduction to Neural Networks.ipynb
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Kernel: Python 3 (ipykernel)

Introduction to Neural Networks

What is a Neural Network?

A Neural Network is a series of algorithms that attempt to recognize underlying relationships in a set of data through a process that mimics the way the human brain operates.

Neural Networks are made of layers:

Input Layer: Receives input data
Hidden Layers: Process the data using weights and activation functions
Output Layer: Produces the final prediction

f(X)=sin(x)

classifcation problem (Accuracy)

Accuracy= TP+TN / FP+FN+TP+TN

1. Binary Classification= sigmoid function 
2. Multi Classifucation = softmax function

Regression: tanhx ,mse

Simple mathematical calculation for a feedforward neural network with:

- 3 inputs
- 2 hidden layers
- 1st hidden layer: 4 neurons
- 2nd hidden layer: 3 neurons

1 output neuron
Using ReLU as the activation function in hidden layers and a linear activation at the output.

We'll calculate the output step-by-step.

1. Input Layer

Let the inputs be:

\mathbf{x} = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 1.0 \\ 0.5 \\ -1.5 \end{bmatrix}

2. Hidden Layer 1 (4 neurons)

Let the weights for the first hidden layer be:

W^{[1]} = \begin{bmatrix} 0.2 & -0.3 & 0.5 \\ -0.4 & 0.1 & -0.2 \\ 0.3 & 0.6 & -0.1 \\ -0.5 & 0.2 & 0.4 \end{bmatrix}, \quad \mathbf{b}^{[1]} = \begin{bmatrix} 0.1 \\ -0.1 \\ 0.2 \\ 0.0 \end{bmatrix}

Calculate $z^{[1]} = W^{[1]} \cdot \mathbf{x} + \mathbf{b}^{[1]}$ :

z^{[1]} = \begin{bmatrix} 0.2 \cdot 1 + (-0.3) \cdot 0.5 + 0.5 \cdot (-1.5) + 0.1 \\ -0.4 \cdot 1 + 0.1 \cdot 0.5 + (-0.2) \cdot (-1.5) - 0.1 \\ 0.3 \cdot 1 + 0.6 \cdot 0.5 + (-0.1) \cdot (-1.5) + 0.2 \\ -0.5 \cdot 1 + 0.2 \cdot 0.5 + 0.4 \cdot (-1.5) + 0 \end{bmatrix} = \begin{bmatrix} 0.2 - 0.15 - 0.75 + 0.1 \\ -0.4 + 0.05 + 0.3 - 0.1 \\ 0.3 + 0.3 + 0.15 + 0.2 \\ -0.5 + 0.1 - 0.6 \end{bmatrix} = \begin{bmatrix} -0.6 \\ -0.15 \\ 0.95 \\ -1.0 \end{bmatrix}

Apply ReLU: $a^{[1]} = \text{ReLU}(z^{[1]}) = \max(0, z^{[1]})$

a^{[1]} = \begin{bmatrix} 0 \\ 0 \\ 0.95 \\ 0 \end{bmatrix}

3. Hidden Layer 2 (3 neurons)

Weights and bias:

W^{[2]} = \begin{bmatrix} 0.1 & -0.2 & 0.3 & 0.4 \\ -0.3 & 0.6 & -0.1 & 0.2 \\ 0.5 & -0.4 & 0.2 & -0.1 \end{bmatrix}, \quad \mathbf{b}^{[2]} = \begin{bmatrix} 0.0 \\ 0.1 \\ -0.2 \end{bmatrix}

Calculate $z^{[2]} = W^{[2]} \cdot a^{[1]} + b^{[2]}$ :

Only the third value of $a^{[1]}$ is nonzero:

z^{[2]} = \begin{bmatrix} 0.3 \cdot 0.95 + 0 \\ -0.1 \cdot 0.95 + 0.1 \\ 0.2 \cdot 0.95 - 0.2 \end{bmatrix} = \begin{bmatrix} 0.285 \\ -0.095 + 0.1 = 0.005 \\ 0.19 - 0.2 = -0.01 \end{bmatrix}

Apply ReLU:

a^{[2]} = \max(0, z^{[2]}) = \begin{bmatrix} 0.285 \\ 0.005 \\ 0 \end{bmatrix}

4. Output Layer (1 neuron)

Weights and bias:

W^{[3]} = \begin{bmatrix} 0.4 & -0.6 & 0.3 \end{bmatrix}, \quad b^{[3]} = 0.05

y = W^{[3]} \cdot a^{[2]} + b^{[3]} = 0.4 \cdot 0.285 - 0.6 \cdot 0.005 + 0.05 = 0.114 - 0.003 + 0.05 = 0.161

Final Output:

\boxed{0.161}

Understanding Neural Networks in Deep Learning

Neural networks are capable of learning and identifying patterns directly from data without pre-defined rules. These networks are built from several key components:

Neurons: The basic units that receive inputs, each neuron is governed by a threshold and an activation function.
Connections: Links between neurons that carry information, regulated by weights and biases.
Weights and Biases: These parameters determine the strength and influence of connections.
Propagation Functions: Mechanisms that help process and transfer data across layers of neurons.
Learning Rule: The method that adjusts weights and biases over time to improve accuracy.

Activation Functions

An activation function is a mathematical operation applied to the output of each neuron in a neural network layer.Without an activation function, a neural network is just a linear function — no matter how many layers you stack:

Example:

𝑊 1 𝑥 + 𝑏 1 ⇒

𝑊 2 ( 𝑊 1 𝑥 + 𝑏 1 ) + 𝑏 2 y=W 1 x+b 1 ⇒y=W 2 (W 1 x+b 1 )+b 2

Activation functions allow the model to learn complex patterns and non-linear relationships.
Helps the Model Learn Complex Mappings Real-world problems (like image recognition, text generation, etc.) are non-linear in nature. Activation functions allow the network to capture such non-linear mappings.
Controls the Output Range Activation functions can:
Limit outputs (e.g., between 0–1 or -1–1)
Introduce probabilities (e.g., softmax in classification)
Help with gradient flow (some functions like ReLU improve training speed and reduce vanishing gradients)

Name	Formula	Output Range	Use Case
ReLU	`f(x) = max(0, x)`	[0, ∞)	Hidden layers (fast & efficient)
Sigmoid	`f(x) = 1 / (1 + e^-x)`	(0, 1)	Binary classification
Tanh	`f(x) = (e^x - e^-x)/(e^x + e^-x)`	(-1, 1)	Can be better than sigmoid
Softmax	`e^xᵢ / Σe^xⱼ`	(0, 1)	Multi-class classification output

In [1]:

# Import Required Libraries
import numpy as np
import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense

Number Sequence Generation Task

Objective: Train a neural network to learn a sequence pattern. Example: 1 → 2, 2 → 3, ..., 9 → 10.

In [5]:

# Prepare training data
X = np.array([i for i in range(1, 51)])
y = np.array([i + 1 for i in range(1, 51)]) #Y=x+1

# Try similar for y=2x, y=x*x go with , 50, 100 

# Reshape input for Keras (samples, features)
X = X.reshape(-1, 1)
y = y.reshape(-1, 1)

In [6]:

Out[6]:

array([[ 1],
       [ 2],
       [ 3],
       [ 4],
       [ 5],
       [ 6],
       [ 7],
       [ 8],
       [ 9],
       [10],
       [11],
       [12],
       [13],
       [14],
       [15],
       [16],
       [17],
       [18],
       [19],
       [20],
       [21],
       [22],
       [23],
       [24],
       [25],
       [26],
       [27],
       [28],
       [29],
       [30],
       [31],
       [32],
       [33],
       [34],
       [35],
       [36],
       [37],
       [38],
       [39],
       [40],
       [41],
       [42],
       [43],
       [44],
       [45],
       [46],
       [47],
       [48],
       [49],
       [50]])

Build a Simple Neural Network

In [7]:

model = Sequential([
    Dense(50, activation='relu', input_shape=(1,)),  # Hidden layer
    Dense(1)  # Output layer
])

# Compile the model
model.compile(optimizer='adam', loss='mse')

# Summary of the model
model.summary()

Out[7]:

C:\Users\Suyashi144893\AppData\Local\anaconda3\Lib\site-packages\keras\src\layers\core\dense.py:87: UserWarning: Do not pass an `input_shape`/`input_dim` argument to a layer. When using Sequential models, prefer using an `Input(shape)` object as the first layer in the model instead.
  super().__init__(activity_regularizer=activity_regularizer, **kwargs)

Train the Model

A epoch is a single pass through the entire training data
After each epoch, the model weights are updated based on training data

Verbose: level of details in every step want to display enter 1 or 2

In [18]:

model.fit(X, y, epochs=300, verbose=1)

Out[18]:

Epoch 1/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step - loss: 0.0142
Epoch 2/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0145  
Epoch 3/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0146
Epoch 4/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0148
Epoch 5/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0147
Epoch 6/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0150
Epoch 7/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0139
Epoch 8/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0140
Epoch 9/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0131
Epoch 10/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0144
Epoch 11/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0140
Epoch 12/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0143
Epoch 13/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0134
Epoch 14/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0143
Epoch 15/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0135 
Epoch 16/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0141
Epoch 17/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0141 
Epoch 18/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0134 
Epoch 19/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0137
Epoch 20/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0134
Epoch 21/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0140 
Epoch 22/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0137
Epoch 23/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0134
Epoch 24/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0139 
Epoch 25/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0140
Epoch 26/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0140
Epoch 27/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0132
Epoch 28/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0134
Epoch 29/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0127
Epoch 30/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0130
Epoch 31/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0132
Epoch 32/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0137
Epoch 33/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0142
Epoch 34/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0143 
Epoch 35/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0134 
Epoch 36/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0144 
Epoch 37/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0136
Epoch 38/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0119
Epoch 39/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0133 
Epoch 40/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0126
Epoch 41/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0135  
Epoch 42/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0135
Epoch 43/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0127
Epoch 44/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0136
Epoch 45/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0134
Epoch 46/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0135  
Epoch 47/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0139
Epoch 48/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0128
Epoch 49/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0130
Epoch 50/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0127
Epoch 51/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0129 
Epoch 52/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0131
Epoch 53/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0133
Epoch 54/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0120
Epoch 55/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0125
Epoch 56/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0125
Epoch 57/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0130
Epoch 58/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0127 
Epoch 59/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0128
Epoch 60/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0126
Epoch 61/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0130
Epoch 62/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0131
Epoch 63/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0134
Epoch 64/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0124
Epoch 65/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0135
Epoch 66/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0122
Epoch 67/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0130
Epoch 68/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0126
Epoch 69/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0128 
Epoch 70/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0125 
Epoch 71/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0123
Epoch 72/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0123
Epoch 73/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0125 
Epoch 74/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0125 
Epoch 75/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0122 
Epoch 76/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0117
Epoch 77/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0131 
Epoch 78/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0124
Epoch 79/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0126
Epoch 80/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0127 
Epoch 81/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0113  
Epoch 82/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0126
Epoch 83/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.01174
Epoch 84/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0128 
Epoch 85/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0116
Epoch 86/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0126 
Epoch 87/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0120
Epoch 88/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0125
Epoch 89/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0121
Epoch 90/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0115
Epoch 91/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0121
Epoch 92/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0119 
Epoch 93/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0122
Epoch 94/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0114
Epoch 95/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0116 
Epoch 96/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0125
Epoch 97/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0118
Epoch 98/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0116
Epoch 99/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0120
Epoch 100/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0118 
Epoch 101/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0118
Epoch 102/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0122
Epoch 103/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0116
Epoch 104/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0127
Epoch 105/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0118
Epoch 106/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0122
Epoch 107/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0119
Epoch 108/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0119
Epoch 109/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0116 
Epoch 110/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0122
Epoch 111/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0119
Epoch 112/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0116
Epoch 113/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0118
Epoch 114/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0122
Epoch 115/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0113
Epoch 116/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0116
Epoch 117/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0115
Epoch 118/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0119
Epoch 119/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0116
Epoch 120/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0114 
Epoch 121/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0120
Epoch 122/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0114
Epoch 123/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0110
Epoch 124/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0114  
Epoch 125/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0120
Epoch 126/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0113 
Epoch 127/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0115
Epoch 128/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0117 
Epoch 129/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0106  
Epoch 130/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0105
Epoch 131/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0114
Epoch 132/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0116
Epoch 133/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0117
Epoch 134/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0110
Epoch 135/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0109
Epoch 136/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0111
Epoch 137/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0115
Epoch 138/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0108
Epoch 139/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0115 
Epoch 140/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0107 
Epoch 141/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0113
Epoch 142/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0104
Epoch 143/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0113
Epoch 144/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0120
Epoch 145/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0102
Epoch 146/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0109
Epoch 147/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0111
Epoch 148/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0105 
Epoch 149/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0109
Epoch 150/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0104 
Epoch 151/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0107
Epoch 152/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0106
Epoch 153/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0112
Epoch 154/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0108 
Epoch 155/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0111 
Epoch 156/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0107  
Epoch 157/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0107
Epoch 158/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0112
Epoch 159/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0105
Epoch 160/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0112
Epoch 161/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0108
Epoch 162/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0101
Epoch 163/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0096 
Epoch 164/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.01072
Epoch 165/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0114 
Epoch 166/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0111
Epoch 167/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0105
Epoch 168/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0105
Epoch 169/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0102
Epoch 170/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0095
Epoch 171/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0090
Epoch 172/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0108
Epoch 173/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - loss: 0.0101
Epoch 174/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0100
Epoch 175/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0101
Epoch 176/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0113
Epoch 177/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - loss: 0.0109
Epoch 178/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0099
Epoch 179/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0099 
Epoch 180/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0101
Epoch 181/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0105
Epoch 182/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - loss: 0.0105
Epoch 183/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0102 
Epoch 184/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - loss: 0.0100
Epoch 185/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0105
Epoch 186/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0103
Epoch 187/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0100
Epoch 188/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0103 
Epoch 189/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0106
Epoch 190/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - loss: 0.0096
Epoch 191/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0096
Epoch 192/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0101 
Epoch 193/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0095
Epoch 194/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0097
Epoch 195/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0098
Epoch 196/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0094
Epoch 197/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0098
Epoch 198/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0092
Epoch 199/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0094 
Epoch 200/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0093
Epoch 201/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0099 
Epoch 202/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0099
Epoch 203/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0094
Epoch 204/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0095
Epoch 205/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0101
Epoch 206/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0098
Epoch 207/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0107
Epoch 208/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0092
Epoch 209/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0100
Epoch 210/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0091 
Epoch 211/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0097
Epoch 212/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0095 
Epoch 213/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0090
Epoch 214/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0100 
Epoch 215/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0095
Epoch 216/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0097
Epoch 217/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0100 
Epoch 218/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0088
Epoch 219/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0090
Epoch 220/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0092
Epoch 221/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0091  
Epoch 222/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0089
Epoch 223/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0090
Epoch 224/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - loss: 0.0087
Epoch 225/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0095  
Epoch 226/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0090 
Epoch 227/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0099  
Epoch 228/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0096  
Epoch 229/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0092 
Epoch 230/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0096 
Epoch 231/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0094
Epoch 232/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0090  
Epoch 233/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0089
Epoch 234/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0087
Epoch 235/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0089  
Epoch 236/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0089  
Epoch 237/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0095
Epoch 238/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0086
Epoch 239/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0090
Epoch 240/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0085
Epoch 241/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0085
Epoch 242/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0090
Epoch 243/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0092
Epoch 244/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0082
Epoch 245/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0086
Epoch 246/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0085 
Epoch 247/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0087
Epoch 248/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0090
Epoch 249/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0086
Epoch 250/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0093
Epoch 251/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0087
Epoch 252/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0089
Epoch 253/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0092
Epoch 254/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0089
Epoch 255/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0079
Epoch 256/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0082
Epoch 257/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0088
Epoch 258/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0086
Epoch 259/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0082 
Epoch 260/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0084 
Epoch 261/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0080  
Epoch 262/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 996us/step - loss: 0.0082
Epoch 263/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0083  
Epoch 264/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0084  
Epoch 265/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0080
Epoch 266/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0079
Epoch 267/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0087
Epoch 268/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0082  
Epoch 269/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0088
Epoch 270/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0082
Epoch 271/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0083
Epoch 272/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0083
Epoch 273/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0080
Epoch 274/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0078
Epoch 275/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0087
Epoch 276/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0086 
Epoch 277/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0086
Epoch 278/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0082 
Epoch 279/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0085
Epoch 280/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0084
Epoch 281/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0086
Epoch 282/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0078 
Epoch 283/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0084 
Epoch 284/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0080
Epoch 285/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0076
Epoch 286/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0080
Epoch 287/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0081
Epoch 288/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0080
Epoch 289/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0076
Epoch 290/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0080 
Epoch 291/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0079
Epoch 292/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0080
Epoch 293/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0082 
Epoch 294/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0083 
Epoch 295/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0075
Epoch 296/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0077
Epoch 297/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0084
Epoch 298/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0076 
Epoch 299/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0074
Epoch 300/300
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0080

<keras.src.callbacks.history.History at 0x11901464dd0>

Test the Model

In [19]:

# Predict the next number in the sequence
test_input = np.array([[150]])
predicted = model.predict(test_input)
print(f"Input: 150 → Predicted Output: {predicted[0][0]:.2f}")

Out[19]:

1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step
Input: 150 → Predicted Output: 151.62

In [ ]: