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Path: blob/master/Generative NLP Models using Python/4 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

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 [6]:

a=[1,23,34]
b=[9,8,7]
a+b
type(a+b)

import numpy as np
a1=np.array(a)
b1=np.array(b)
a1+b1
a1/b1
a1*b1

Out[6]:

array([  9, 184, 238])

In [7]:

# 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 [11]:

# Prepare training data
X = np.array([i for i in range(1, 50)])
y = np.array([i + 1 for i in range(1, 50)])

# 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 [12]:

X
y

Out[12]:

array([[ 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 [13]:

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[13]:

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 [16]:

model.fit(X, y, epochs=250, verbose=1)

Out[16]:

Epoch 1/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - loss: 0.0133
Epoch 2/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 9ms/step - loss: 0.0130
Epoch 3/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0141
Epoch 4/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0128   
Epoch 5/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0125   
Epoch 6/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0144
Epoch 7/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0139
Epoch 8/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0134  
Epoch 9/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0131  
Epoch 10/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0128  
Epoch 11/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0134
Epoch 12/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0131  
Epoch 13/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0143   
Epoch 14/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0131
Epoch 15/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0124  
Epoch 16/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0138
Epoch 17/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0129
Epoch 18/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0138  
Epoch 19/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0128 
Epoch 20/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0137  
Epoch 21/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0138 
Epoch 22/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0120
Epoch 23/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0140   
Epoch 24/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0140
Epoch 25/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0132 
Epoch 26/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0123
Epoch 27/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0133 
Epoch 28/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0137
Epoch 29/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0130
Epoch 30/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0128 
Epoch 31/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0125
Epoch 32/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0134 
Epoch 33/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0116  
Epoch 34/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0126
Epoch 35/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0130
Epoch 36/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0133
Epoch 37/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0133  
Epoch 38/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0125
Epoch 39/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0125  
Epoch 40/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0129
Epoch 41/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0124
Epoch 42/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0112  
Epoch 43/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0129  
Epoch 44/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0119
Epoch 45/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0131
Epoch 46/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - loss: 0.0128 
Epoch 47/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0127 
Epoch 48/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0130
Epoch 49/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0127
Epoch 50/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0128
Epoch 51/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0125 
Epoch 52/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0125
Epoch 53/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0119
Epoch 54/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0128
Epoch 55/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0121
Epoch 56/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0122
Epoch 57/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0122
Epoch 58/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0130
Epoch 59/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0123
Epoch 60/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0126
Epoch 61/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0118
Epoch 62/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0124
Epoch 63/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0120  
Epoch 64/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0123 
Epoch 65/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - loss: 0.0123
Epoch 66/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0123
Epoch 67/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0126
Epoch 68/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0122 
Epoch 69/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0129
Epoch 70/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0119 
Epoch 71/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0128
Epoch 72/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0115
Epoch 73/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0118
Epoch 74/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0125
Epoch 75/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0124 
Epoch 76/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0124
Epoch 77/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0121
Epoch 78/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0122
Epoch 79/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0119
Epoch 80/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0112
Epoch 81/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0118
Epoch 82/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0126 
Epoch 83/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0123
Epoch 84/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0123
Epoch 85/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0123
Epoch 86/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0126
Epoch 87/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0114
Epoch 88/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0125 
Epoch 89/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0115
Epoch 90/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0115 
Epoch 91/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0123
Epoch 92/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0124
Epoch 93/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0114
Epoch 94/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0119
Epoch 95/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0115
Epoch 96/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0115
Epoch 97/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0113
Epoch 98/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0108
Epoch 99/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0121  
Epoch 100/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0115 
Epoch 101/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0115
Epoch 102/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0127 
Epoch 103/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0119
Epoch 104/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0118
Epoch 105/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0118
Epoch 106/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0114
Epoch 107/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0115
Epoch 108/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0111
Epoch 109/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0116
Epoch 110/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0116
Epoch 111/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0113
Epoch 112/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0115
Epoch 113/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0116
Epoch 114/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0112
Epoch 115/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0115 
Epoch 116/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0119
Epoch 117/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0112
Epoch 118/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0115
Epoch 119/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0104
Epoch 120/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0110 
Epoch 121/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0120
Epoch 122/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0114
Epoch 123/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0116
Epoch 124/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0115
Epoch 125/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0107
Epoch 126/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0115 
Epoch 127/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0109
Epoch 128/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0115
Epoch 129/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0108 
Epoch 130/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0116 
Epoch 131/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0116
Epoch 132/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0112
Epoch 133/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0115
Epoch 134/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0112
Epoch 135/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0116
Epoch 136/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0109
Epoch 137/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0105
Epoch 138/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0109
Epoch 139/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0107
Epoch 140/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0110 
Epoch 141/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0110 
Epoch 142/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0111
Epoch 143/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0117
Epoch 144/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0106
Epoch 145/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0107
Epoch 146/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0114
Epoch 147/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0112
Epoch 148/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0104
Epoch 149/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0107 
Epoch 150/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0110
Epoch 151/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0106
Epoch 152/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0109
Epoch 153/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0107
Epoch 154/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0109 
Epoch 155/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0103
Epoch 156/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0111
Epoch 157/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0100
Epoch 158/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0106 
Epoch 159/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0105
Epoch 160/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0106
Epoch 161/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 10ms/step - loss: 0.0107
Epoch 162/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0099
Epoch 163/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0108
Epoch 164/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0109 
Epoch 165/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0101
Epoch 166/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0103
Epoch 167/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0101
Epoch 168/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0104 
Epoch 169/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0106
Epoch 170/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0096
Epoch 171/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0110
Epoch 172/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0103
Epoch 173/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0103 
Epoch 174/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0099
Epoch 175/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0104
Epoch 176/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 7ms/step - loss: 0.0107
Epoch 177/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - loss: 0.0102 
Epoch 178/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0106 
Epoch 179/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0101 
Epoch 180/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0115
Epoch 181/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0105
Epoch 182/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0097
Epoch 183/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0097 
Epoch 184/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0110
Epoch 185/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0102
Epoch 186/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0100
Epoch 187/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0104
Epoch 188/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0106
Epoch 189/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0099
Epoch 190/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0101
Epoch 191/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0108
Epoch 192/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0105 
Epoch 193/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0105
Epoch 194/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0102
Epoch 195/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0102 
Epoch 196/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0099
Epoch 197/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0096
Epoch 198/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0094
Epoch 199/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0097
Epoch 200/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0104
Epoch 201/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0098 
Epoch 202/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0096
Epoch 203/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0098
Epoch 204/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0099
Epoch 205/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0097
Epoch 206/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0100
Epoch 207/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0096
Epoch 208/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0092 
Epoch 209/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0096 
Epoch 210/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0104
Epoch 211/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0101
Epoch 212/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0095
Epoch 213/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0096
Epoch 214/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0102
Epoch 215/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0093
Epoch 216/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0100
Epoch 217/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0097
Epoch 218/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0099
Epoch 219/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0102
Epoch 220/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0098
Epoch 221/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0093 
Epoch 222/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - loss: 0.0091
Epoch 223/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0101
Epoch 224/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0103
Epoch 225/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0095 
Epoch 226/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0096
Epoch 227/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0101
Epoch 228/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0095
Epoch 229/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0096 
Epoch 230/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0097
Epoch 231/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0089
Epoch 232/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0100 
Epoch 233/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0099
Epoch 234/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0092
Epoch 235/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0093 
Epoch 236/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.0101
Epoch 237/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0090
Epoch 238/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0098
Epoch 239/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0099
Epoch 240/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0088
Epoch 241/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0094
Epoch 242/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0090
Epoch 243/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0091
Epoch 244/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0093
Epoch 245/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0094
Epoch 246/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.00948
Epoch 247/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0088
Epoch 248/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0091
Epoch 249/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - loss: 0.0091 
Epoch 250/250
2/2 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0092

<keras.src.callbacks.history.History at 0x1ca9e275750>

Test the Model

In [21]:

# Predict the next number in the sequence
test_input = np.array([[100]])
predicted = model.predict(test_input)
print(f"Input: 11 → Predicted Output: {predicted[0][0]:.2f}")

Out[21]:

1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 46ms/step
Input: 11 → Predicted Output: 101.39