The document discusses output activation and loss functions for neural networks. It provides an overview of common activation functions used for the output layer like sigmoid, tanh, softmax and rectified linear units. It also reviews loss functions like squared error loss and cross entropy loss defined based on the network's output activation. The loss functions guide the weight updates in the network during training to minimize error.
Introduction to Neural Networks and Deep Learning from ScratchAhmed BESBES
If you're willing to understand how neural networks work behind the scene and debug the back-propagation algorithm step by step by yourself, this presentation should be a good starting point.
We'll cover elements on:
- the popularity of neural networks and their applications
- the artificial neuron and the analogy with the biological one
- the perceptron
- the architecture of multi-layer perceptrons
- loss functions
- activation functions
- the gradient descent algorithm
At the end, there will be an implementation FROM SCRATCH of a fully functioning neural net.
code: https://github.com/ahmedbesbes/Neural-Network-from-scratch
Direct solution of sparse network equations by optimally ordered triangular f...Dimas Ruliandi
Triangular factorization method of a power network problem (in form of matrix). Direct solution can be found without calculating inverse matrix which usually considered an exhaustive method, especially in large scale network.
Introduction to Neural Networks and Deep Learning from ScratchAhmed BESBES
If you're willing to understand how neural networks work behind the scene and debug the back-propagation algorithm step by step by yourself, this presentation should be a good starting point.
We'll cover elements on:
- the popularity of neural networks and their applications
- the artificial neuron and the analogy with the biological one
- the perceptron
- the architecture of multi-layer perceptrons
- loss functions
- activation functions
- the gradient descent algorithm
At the end, there will be an implementation FROM SCRATCH of a fully functioning neural net.
code: https://github.com/ahmedbesbes/Neural-Network-from-scratch
Direct solution of sparse network equations by optimally ordered triangular f...Dimas Ruliandi
Triangular factorization method of a power network problem (in form of matrix). Direct solution can be found without calculating inverse matrix which usually considered an exhaustive method, especially in large scale network.
Basic concept of Deep Learning with explaining its structure and backpropagation method and understanding autograd in PyTorch. (+ Data parallism in PyTorch)
Umbra Ignite 2015: Rulon Raymond – The State of Skinning – a dive into modern...Umbra Software
Rulon Raymond was the keynote speaker of Umbra Ignite. His talk “The State of Skinning – a dive into modern approaches to model skinning” leads us in to a quick yet deep journey through real time skinning trends.
Utilitas Mathematica Journal original research and review articles. Utilitas Mathematica Journal commits to strengthening our professional community by making it more just, equitable, diverse, and inclusive. Algebra ,Analysis ,Geometry Offers selected original research in Pure and Applied Mathematics and Statistics.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
Basic concept of Deep Learning with explaining its structure and backpropagation method and understanding autograd in PyTorch. (+ Data parallism in PyTorch)
Umbra Ignite 2015: Rulon Raymond – The State of Skinning – a dive into modern...Umbra Software
Rulon Raymond was the keynote speaker of Umbra Ignite. His talk “The State of Skinning – a dive into modern approaches to model skinning” leads us in to a quick yet deep journey through real time skinning trends.
Utilitas Mathematica Journal original research and review articles. Utilitas Mathematica Journal commits to strengthening our professional community by making it more just, equitable, diverse, and inclusive. Algebra ,Analysis ,Geometry Offers selected original research in Pure and Applied Mathematics and Statistics.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Water billing management system project report.pdfKamal Acharya
Our project entitled “Water Billing Management System” aims is to generate Water bill with all the charges and penalty. Manual system that is employed is extremely laborious and quite inadequate. It only makes the process more difficult and hard.
The aim of our project is to develop a system that is meant to partially computerize the work performed in the Water Board like generating monthly Water bill, record of consuming unit of water, store record of the customer and previous unpaid record.
We used HTML/PHP as front end and MYSQL as back end for developing our project. HTML is primarily a visual design environment. We can create a android application by designing the form and that make up the user interface. Adding android application code to the form and the objects such as buttons and text boxes on them and adding any required support code in additional modular.
MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software. It is a stable ,reliable and the powerful solution with the advanced features and advantages which are as follows: Data Security.MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software.
An Approach to Detecting Writing Styles Based on Clustering Techniquesambekarshweta25
An Approach to Detecting Writing Styles Based on Clustering Techniques
Authors:
-Devkinandan Jagtap
-Shweta Ambekar
-Harshit Singh
-Nakul Sharma (Assistant Professor)
Institution:
VIIT Pune, India
Abstract:
This paper proposes a system to differentiate between human-generated and AI-generated texts using stylometric analysis. The system analyzes text files and classifies writing styles by employing various clustering algorithms, such as k-means, k-means++, hierarchical, and DBSCAN. The effectiveness of these algorithms is measured using silhouette scores. The system successfully identifies distinct writing styles within documents, demonstrating its potential for plagiarism detection.
Introduction:
Stylometry, the study of linguistic and structural features in texts, is used for tasks like plagiarism detection, genre separation, and author verification. This paper leverages stylometric analysis to identify different writing styles and improve plagiarism detection methods.
Methodology:
The system includes data collection, preprocessing, feature extraction, dimensional reduction, machine learning models for clustering, and performance comparison using silhouette scores. Feature extraction focuses on lexical features, vocabulary richness, and readability scores. The study uses a small dataset of texts from various authors and employs algorithms like k-means, k-means++, hierarchical clustering, and DBSCAN for clustering.
Results:
Experiments show that the system effectively identifies writing styles, with silhouette scores indicating reasonable to strong clustering when k=2. As the number of clusters increases, the silhouette scores decrease, indicating a drop in accuracy. K-means and k-means++ perform similarly, while hierarchical clustering is less optimized.
Conclusion and Future Work:
The system works well for distinguishing writing styles with two clusters but becomes less accurate as the number of clusters increases. Future research could focus on adding more parameters and optimizing the methodology to improve accuracy with higher cluster values. This system can enhance existing plagiarism detection tools, especially in academic settings.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
1. Output Activation and Loss Functions
✓ Every neural net specifies
▪ an activation rule for the output unit(s)
▪ a loss defined in terms of the output activation
✓ First a bit of review…
2. Cheat Sheet 1
✓ Perceptron
▪ Activation function
▪ Weight update
✓
Linear associator (a.k.a. linear regression)
▪ Activation function
▪ Weight update
zj = wjixi
i
å yj =
1 if zj > 0
0 otherwise
ì
í
ï
î
ï
Dwji = (tj - yj )xi tj Î{0,1}
yj = wjixi
i
å
Dwji = e(tj - yj )xi tj λ
assumes minimizing
squarederror loss
assumes minimizing
numberof
misclassifications
3. Cheat Sheet 2
✓ Two layer net (a.k.a. logistic regression)
▪ activation function
▪ weight update
✓ Deep(er) net
▪ activation function same as above
▪ weight update
zj = wjixi
i
å yj =
1
1+ exp(-zj )
Dwji = e(tj - yj )yj (1- yj )xi tj Î 0,1
[ ]
assumes minimizing
squarederror loss
Dwji = ed j xi d j =
(tj - yj )yj (1- yj ) for output unit
wkjdk
k
å
æ
è
ç
ö
ø
÷ yj (1- yj ) for hidden unit
ì
í
ï
ï
î
ï
ï
assumes minimizing
squarederror loss
4. Squared Error Loss
✓ Sensible regardless of output range and output activation function
✓
▪ with logistic output unit
▪ with tanh output unit
yj =
1
1+ exp(-zj )
𝜕𝑦𝑗
𝜕𝑧𝑗
= 𝑦𝑗 1 − 𝑦𝑗
𝜕𝑦𝑗
𝜕𝑧𝑗
= 1 + 𝑦𝑗 1 − 𝑦𝑗
𝑦𝑗 = tanh 𝑧𝑗
=
2
1 + exp(−𝑧𝑗)
− 1
E =
1
2
tj - yj
( )
2
j
å 𝜕𝐸
𝜕𝑦𝑗
= 𝑦𝑗 − 𝑡𝑗
Remember
𝚫𝐰 = −𝝐
𝝏𝑬
𝝏𝒚
…
5. Logistic vs. Tanh
•Output = .5
▪ when no inputevidence,bias=0
•Will trigger activation in next layer
•Need large biases to neutralize
▪ biaseson differentscale than other
weights
•Does not satisfy weight
initialization assumption of mean
activation = 0
•Output = 0
▪ when no inputevidence,bias=0
•Won’t trigger activation in next
layer
•Don’t need large biases
•Satisfies weight initialization
assumption
6. Cross Entropy Loss
✓ Used when the target output represents a probability distribution
▪ e.g., a single output unit that indicates the classification decision (yes, no) for an
input
Output𝒚 ∈ [𝟎,𝟏] denotesBernoullilikelihoodof class membership
Target 𝒕 indicatestrue class probability(typically0 or 1)
Note: single valuerepresentsprobability distribution over 2 alternatives
✓ Cross entropy, 𝑯, measures distance in bits from predicted distribution to target
distribution
✓
𝐸 = 𝐻 = −𝑡ln 𝑦 − 1 − 𝑡 ln 1 − 𝑦
𝜕𝐸
𝜕𝑦
=
𝑦 − 𝑡
𝑦(1 − 𝑦)
8. Maximum Likelihood Estimation
✓ In statistics, many parameter estimation problems are formulated in terms of
maximizing the likelihood of the data
▪ find model parameters that maximize the likelihood of the data under the model
▪ e.g., 10 coin flips producing 8 heads and 2 tails
What is the coin’s bias?
✓ Likelihood formulation
▪ ℒ = 𝒚𝒕
𝟏 − 𝒚 𝟏−𝒕
for 𝒕 ∈ 𝟎,𝟏
▪ ℓ = ln ℒ = 𝒕ln 𝒚 + 𝟏 − 𝒕 ln 𝟏 − 𝒚
What’s the relationship
between ℓ and 𝑬xentropy?
9. Probabilistic Interpretation of Squared-Error Loss
✓ Consider a network output and target 𝒚, 𝒕 ∈ ℝ
✓ Suppose that the output is corrupted by Gaussian observation noise
▪ 𝒚 = 𝒕 + 𝜼
▪ where 𝜼 ~ Gaussian 𝟎,𝟏
✓ We can define the likelihood of the target under this noise model
▪ 𝑷 𝒕 𝒚 =
𝟏
𝟐𝝅
𝐞𝐱𝐩 −
𝟏
𝟐
𝒕 − 𝒚 𝟐
𝒚
10. Probabilistic Interpretation of Squared-Error Loss
✓ For a set of training examples, 𝜶 ∈ {𝟏,𝟐,𝟑, … }, we can definethe data set likelihood
▪ ℒ = ς𝜶 𝑷 𝒕𝜶
𝒚𝜶
▪ ℓ = 𝐥𝐧ℒ = σ𝜶 𝐥𝐧𝑷(𝒕𝜶
|𝒚𝜶
) where 𝑷 𝒕 𝒚 =
𝟏
𝟐𝝅
𝐞𝐱𝐩 −
𝟏
𝟐
𝒕 − 𝒚 𝟐
▪ = −
𝟏
𝟐
σ𝜶 𝒕𝜶
− 𝒚𝜶 𝟐
✓ Squarederror can be viewedas likelihoodunder Gaussian observationnoise
▪ 𝑬𝐬𝐪𝐞𝐫𝐫 = −𝒄ℓ
✓ Other noise distributionscan motivatealternativelosses.
▪ e.g., Laplace distributed noise and 𝑬𝐚𝐛𝐬𝐞𝐫𝐫 = 𝒕 − 𝒚
What is
𝝏𝑬𝐚𝐛𝐬𝐞𝐫𝐫
𝝏𝒚
?
11. Categorical Outputs
✓ We considered the case where the output 𝒚 denotes the probability of
class membership
▪ belonging to class 𝑨 versus ഥ
𝑨
✓ Instead of two possible categories, suppose there are n
▪ e.g., animal, vegetable, mineral
12. Categorical Outputs
✓ Each input can belong to one category
▪ 𝒚𝒋 denotes the probability that the input’s category is 𝒋
✓ To interpret 𝒚 as a probability distribution over the alternatives
▪ σ𝒋 𝒚𝒋 = 𝟏 and 𝟎 ≤ 𝒚𝒋 ≤ 𝟏
✓ Activation function
▪ 𝒚𝒋 =
exp 𝒛𝒋
σ𝒌 exp 𝒛𝒌
Exponentiationensuresnonnegativevalues
Denominatorensuressum to 1
✓ Known as softmax, and formerly, Luce choice rule
13. Derivatives For Categorical Outputs
✓ For softmax output function
✓ Weight update is the same as for two-category case!
✓ …when expressed in terms of 𝒚
yj =
exp(zj )
exp(zk )
k
å
Dwji = ed j xi d j =
¶E
¶yj
yj (1- yj ) for output unit
wkjdk
k
å
æ
è
ç
ö
ø
÷ yj (1- yj ) for hidden unit
ì
í
ï
ï
î
ï
ï
zj = wjixi
i
å
14. Rectified Linear Unit (ReLU)
✓ Activationfunction Derivative
▪ 𝒚 = max(𝟎, 𝒛)
𝝏𝒚
𝝏𝒛
= ቊ
𝟎 𝒛 ≤ 𝟎
𝟏 𝐨𝐭𝐡𝐞𝐫𝐰𝐢𝐬𝐞
✓ Advantages
▪ fast to compute activationand derivatives
▪ no squashing of back propagated error signal as long as unit is activated
▪ discontinuity in derivative at z=0
▪ sparsity ?
✓ Disadvantages
▪ can potentially lead to exploding gradients and activations
▪ may waste units: units that are never activatedabove threshold won’t learn
𝒛
𝒚
15. Leaky ReLU
✓ Activation function Derivative
✓ Reduces to standard ReLU if 𝜶 = 𝟎
✓ Trade off
▪ 𝜶 = 𝟎 leads to inefficient use of resources (underutilized units)
▪ 𝜶 = 𝟏 lose nonlinearity essential for interesting computation
𝒛
𝒚
16. Softplus
✓ Activation function Derivative
▪ 𝒚 = 𝐥𝐧 𝟏 + 𝒆𝒛 𝝏𝒚
𝝏𝒛
=
𝟏
𝟏+𝒆−𝒛
= 𝐥𝐨𝐠𝐢𝐬𝐭𝐢𝐜 𝒛
✓Derivative
▪ defined everywhere
▪ zero only for 𝒛 → −∞
𝒛
𝒚
17. Exponential Linear Unit (ELU)
✓ Activation function Derivative
✓ Reduces to standard ReLU if 𝜶 = 𝟎
𝒛
𝒚
𝒛
𝒚
18. Radial Basis Functions
✓ Activation function
▪ 𝒚 = exp − 𝒙 − 𝒘 𝟐
✓ Sparse activation
▪ many units just don’t learn
▪ same issue as ReLUs
✓ Clever schemes to initialize weights
▪ e.g., set 𝒘 near cluster of 𝒙’s
𝒙
𝒘
Image credits: www.dtreg.com
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