An approximate introduction to how zk-SNARKs are possible (part 2)
If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.
Polynomials
Polynomials are a special class of algebraic expressions of the form:
- x+5
- x^4
- x^3+3x^2+3x+1
- 628x^{271}+318x^{270}+530x^{269}+…+69x+381
i.e. they are a sum of any (finite!) number of terms of the form cx^k
There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.
Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:
- A(0)+B(0)=C(0)
- A(1)+B(1)=C(1)
- A(2)+B(2)=C(2)
- A(3)+B(3)=C(3)
And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:
- 12+1=13
- 10+8=18
- 15+8=23
- 15+13=28
You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:
- A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
- B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
- C(x)=5x+13
Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.
Comparing a polynomial to itself
You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)
As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.
Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).
Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!
Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.
see part 3
(Edited)

Hackernoon
3 years ago
👏 Awesome post! When is part 3 coming?

Trent Lapinski
3 years ago
Very complex topic, great explanation
More on Web3 & Crypto
James Howell
3 years ago
Which Metaverse Is Better, Decentraland or Sandbox?
The metaverse is the most commonly used term in current technology discussions. While the entire tech ecosystem awaits the metaverse's full arrival, defining it is difficult. Imagine the internet in the '80s! The metaverse is a three-dimensional virtual world where users can interact with digital solutions and each other as digital avatars.
The metaverse is a three-dimensional virtual world where users can interact with digital solutions and each other as digital avatars.
Among the metaverse hype, the Decentraland vs Sandbox debate has gained traction. Both are decentralized metaverse platforms with no central authority. So, what's the difference and which is better? Let us examine the distinctions between Decentraland and Sandbox.
2 Popular Metaverse Platforms Explained
The first step in comparing sandbox and Decentraland is to outline the definitions. Anyone keeping up with the metaverse news has heard of the two current leaders. Both have many similarities, but also many differences. Let us start with defining both platforms to see if there is a winner.
Decentraland
Decentraland, a fully immersive and engaging 3D metaverse, launched in 2017. It allows players to buy land while exploring the vast virtual universe. Decentraland offers a wide range of activities for its visitors, including games, casinos, galleries, and concerts. It is currently the longest-running metaverse project.
Decentraland began with a $24 million ICO and went public in 2020. The platform's virtual real estate parcels allow users to create a variety of experiences. MANA and LAND are two distinct tokens associated with Decentraland. MANA is the platform's native ERC-20 token, and users can burn MANA to get LAND, which is ERC-721 compliant. The MANA coin can be used to buy avatars, wearables, products, and names on Decentraland.
Sandbox
Sandbox, the next major player, began as a blockchain-based virtual world in 2011 and migrated to a 3D gaming platform in 2017. The virtual world allows users to create, play, own, and monetize their virtual experiences. Sandbox aims to empower artists, creators, and players in the blockchain community to customize the platform. Sandbox gives the ideal means for unleashing creativity in the development of the modern gaming ecosystem.
The project combines NFTs and DAOs to empower a growing community of gamers. A new play-to-earn model helps users grow as gamers and creators. The platform offers a utility token, SAND, which is required for all transactions.
What are the key points from both metaverse definitions to compare Decentraland vs sandbox?
It is ideal for individuals, businesses, and creators seeking new artistic, entertainment, and business opportunities. It is one of the rapidly growing Decentralized Autonomous Organization projects. Holders of MANA tokens also control the Decentraland domain.
Sandbox, on the other hand, is a blockchain-based virtual world that runs on the native token SAND. On the platform, users can create, sell, and buy digital assets and experiences, enabling blockchain-based gaming. Sandbox focuses on user-generated content and building an ecosystem of developers.
Sandbox vs. Decentraland
If you try to find what is better Sandbox or Decentraland, then you might struggle with only the basic definitions. Both are metaverse platforms offering immersive 3D experiences. Users can freely create, buy, sell, and trade digital assets. However, both have significant differences, especially in MANA vs SAND.
For starters, MANA has a market cap of $5,736,097,349 versus $4,528,715,461, giving Decentraland an advantage.
The MANA vs SAND pricing comparison is also noteworthy. A SAND is currently worth $3664, while a MANA is worth $2452.
The value of the native tokens and the market capitalization of the two metaverse platforms are not enough to make a choice. Let us compare Sandbox vs Decentraland based on the following factors.
Workstyle
The way Decentraland and Sandbox work is one of the main comparisons. From a distance, they both appear to work the same way. But there's a lot more to learn about both platforms' workings. Decentraland has 90,601 digital parcels of land.
Individual parcels of virtual real estate or estates with multiple parcels of land are assembled. It also has districts with similar themes and plazas, which are non-tradeable parcels owned by the community. It has three token types: MANA, LAND, and WEAR.
Sandbox has 166,464 plots of virtual land that can be grouped into estates. Estates are owned by one person, while districts are owned by two or more people. The Sandbox metaverse has four token types: SAND, GAMES, LAND, and ASSETS.
Age
The maturity of metaverse projects is also a factor in the debate. Decentraland is clearly the winner in terms of maturity. It was the first solution to create a 3D blockchain metaverse. Decentraland made the first working proof of concept public. However, Sandbox has only made an Alpha version available to the public.
Backing
The MANA vs SAND comparison would also include support for both platforms. Digital Currency Group, FBG Capital, and CoinFund are all supporters of Decentraland. It has also partnered with Polygon, the South Korean government, Cyberpunk, and Samsung.
SoftBank, a Japanese multinational conglomerate focused on investment management, is another major backer. Sandbox has the backing of one of the world's largest investment firms, as well as Slack and Uber.
Compatibility
Wallet compatibility is an important factor in comparing the two metaverse platforms. Decentraland currently has a competitive advantage. How? Both projects' marketplaces accept ERC-20 wallets. However, Decentraland has recently improved by bridging with Walletconnect. So it can let Polygon users join Decentraland.
Scalability
Because Sandbox and Decentraland use the Ethereum blockchain, scalability is an issue. Both platforms' scalability is constrained by volatile tokens and high gas fees. So, scalability issues can hinder large-scale adoption of both metaverse platforms.
Buying Land
Decentraland vs Sandbox comparisons often include virtual real estate. However, the ability to buy virtual land on both platforms defines the user experience and differentiates them. In this case, Sandbox offers better options for users to buy virtual land by combining OpenSea and Sandbox. In fact, Decentraland users can only buy from the MANA marketplace.
Innovation
The rate of development distinguishes Sandbox and Decentraland. Both platforms have been developing rapidly new features. However, Sandbox wins by adopting Polygon NFT layer 2 solutions, which consume almost 100 times less energy than Ethereum.
Collaborations
The platforms' collaborations are the key to determining "which is better Sandbox or Decentraland." Adoption of metaverse platforms like the two in question can be boosted by association with reputable brands. Among the partners are Atari, Cyberpunk, and Polygon. Rather, Sandbox has partnered with well-known brands like OpenSea, CryptoKitties, The Walking Dead, Snoop Dogg, and others.
Platform Adaptivity
Another key feature that distinguishes Sandbox and Decentraland is the ease of use. Sandbox clearly wins in terms of platform access. It allows easy access via social media, email, or a Metamask wallet. However, Decentraland requires a wallet connection.
Prospects
The future development plans also play a big role in defining Sandbox vs Decentraland. Sandbox's future development plans include bringing the platform to mobile devices. This includes consoles like PlayStation and Xbox. By the end of 2023, the platform expects to have around 5000 games.
Decentraland, on the other hand, has no set plan. In fact, the team defines the decisions that appear to have value. They plan to add celebrities, creators, and brands soon, along with NFT ads and drops.
Final Words
The comparison of Decentraland vs Sandbox provides a balanced view of both platforms. You can see how difficult it is to determine which decentralized metaverse is better now. Sandbox is still in Alpha, whereas Decentraland has a working proof of concept.
Sandbox, on the other hand, has better graphics and is backed by some big names. But both have a long way to go in the larger decentralized metaverse.

Shan Vernekar
3 years ago
How the Ethereum blockchain's transactions are carried out
Overview
Ethereum blockchain is a network of nodes that validate transactions. Any network node can be queried for blockchain data for free. To write data as a transition requires processing and writing to each network node's storage. Fee is paid in ether and is also called as gas.
We'll examine how user-initiated transactions flow across the network and into the blockchain.
Flow of transactions
A user wishes to move some ether from one external account to another. He utilizes a cryptocurrency wallet for this (like Metamask), which is a browser extension.
The user enters the desired transfer amount and the external account's address. He has the option to choose the transaction cost he is ready to pay.
Wallet makes use of this data, signs it with the user's private key, and writes it to an Ethereum node. Services such as Infura offer APIs that enable writing data to nodes. One of these services is used by Metamask. An example transaction is shown below. Notice the “to” address and value fields.
var rawTxn = {
nonce: web3.toHex(txnCount),
gasPrice: web3.toHex(100000000000),
gasLimit: web3.toHex(140000),
to: '0x633296baebc20f33ac2e1c1b105d7cd1f6a0718b',
value: web3.toHex(0),
data: '0xcc9ab24952616d6100000000000000000000000000000000000000000000000000000000'
};The transaction is written to the target Ethereum node's local TRANSACTION POOL. It informed surrounding nodes of the new transaction, and those nodes reciprocated. Eventually, this transaction is received by and written to each node's local TRANSACTION pool.
The miner who finds the following block first adds pending transactions (with a higher gas cost) from the nearby TRANSACTION POOL to the block.
The transactions written to the new block are verified by other network nodes.
A block is added to the main blockchain after there is consensus and it is determined to be genuine. The local blockchain is updated with the new node by additional nodes as well.
Block mining begins again next.
The image above shows how transactions go via the network and what's needed to submit them to the main block chain.
References
ethereum.org/transactions How Ethereum transactions function, their data structure, and how to send them via app. ethereum.org

Rishi Dean
3 years ago
Coinbase's web3 app
Use popular Ethereum dapps with Coinbase’s new dapp wallet and browser
Tl;dr: This post highlights the ability to access web3 directly from your Coinbase app using our new dapp wallet and browser.
Decentralized autonomous organizations (DAOs) and decentralized finance (DeFi) have gained popularity in the last year (DAOs). The total value locked (TVL) of DeFi investments on the Ethereum blockchain has grown to over $110B USD, while NFTs sales have grown to over $30B USD in the last 12 months (LTM). New innovative real-world applications are emerging every day.
Today, a small group of Coinbase app users can access Ethereum-based dapps. Buying NFTs on Coinbase NFT and OpenSea, trading on Uniswap and Sushiswap, and borrowing and lending on Curve and Compound are examples.
Our new dapp wallet and dapp browser enable you to access and explore web3 directly from your Coinbase app.
Web3 in the Coinbase app
Users can now access dapps without a recovery phrase. This innovative dapp wallet experience uses Multi-Party Computation (MPC) technology to secure your on-chain wallet. This wallet's design allows you and Coinbase to share the 'key.' If you lose access to your device, the key to your dapp wallet is still safe and Coinbase can help recover it.
Set up your new dapp wallet by clicking the "Browser" tab in the Android app's navigation bar. Once set up, the Coinbase app's new dapp browser lets you search, discover, and use Ethereum-based dapps.
Looking forward
We want to enable everyone to seamlessly and safely participate in web3, and today’s launch is another step on that journey. We're rolling out the new dapp wallet and browser in the US on Android first to a small subset of users and plan to expand soon. Stay tuned!
You might also like

Nicolas Tresegnie
3 years ago
Launching 10 SaaS applications in 100 days
Apocodes helps entrepreneurs create SaaS products without writing code. This post introduces micro-SaaS and outlines its basic strategy.
Strategy
Vision and strategy differ when starting a startup.
The company's long-term future state is outlined in the vision. It establishes the overarching objectives the organization aims to achieve while also justifying its existence. The company's future is outlined in the vision.
The strategy consists of a collection of short- to mid-term objectives, the accomplishment of which will move the business closer to its vision. The company gets there through its strategy.
The vision should be stable, but the strategy must be adjusted based on customer input, market conditions, or previous experiments.
Begin modestly and aim high.
Be truthful. It's impossible to automate SaaS product creation from scratch. It's like climbing Everest without running a 5K. Physical rules don't prohibit it, but it would be suicide.
Apocodes 5K equivalent? Two options:
(A) Create a feature that includes every setting option conceivable. then query potential clients “Would you choose us to build your SaaS solution if we offered 99 additional features of the same caliber?” After that, decide which major feature to implement next.
(B) Build a few straightforward features with just one or two configuration options. Then query potential clients “Will this suffice to make your product?” What's missing if not? Finally, tweak the final result a bit before starting over.
(A) is an all-or-nothing approach. It's like training your left arm to climb Mount Everest. My right foot is next.
(B) is a better method because it's iterative and provides value to customers throughout.
Focus on a small market sector, meet its needs, and expand gradually. Micro-SaaS is Apocode's first market.
What is micro-SaaS.
Micro-SaaS enterprises have these characteristics:
A limited range: They address a specific problem with a small number of features.
A small group of one to five individuals.
Low external funding: The majority of micro-SaaS companies have Total Addressable Markets (TAM) under $100 million. Investors find them unattractive as a result. As a result, the majority of micro-SaaS companies are self-funded or bootstrapped.
Low competition: Because they solve problems that larger firms would rather not spend time on, micro-SaaS enterprises have little rivalry.
Low upkeep: Because of their simplicity, they require little care.
Huge profitability: Because providing more clients incurs such a small incremental cost, high profit margins are possible.
Micro-SaaS enterprises created with no-code are Apocode's ideal first market niche.
We'll create our own micro-SaaS solutions to better understand their needs. Although not required, we believe this will improve community discussions.
The challenge
In 100 days (September 12–December 20, 2022), we plan to build 10 micro-SaaS enterprises using Apocode.
They will be:
Self-serve: Customers will be able to use the entire product experience without our manual assistance.
Real: They'll deal with actual issues. They won't be isolated proofs of concept because we'll keep up with them after the challenge.
Both free and paid options: including a free plan and a free trial period. Although financial success would be a good result, the challenge's stated objective is not financial success.
This will let us design Apocodes features, showcase them, and talk to customers.
(Edit: The first micro-SaaS was launched!)
Follow along
If you want to follow the story of Apocode or our progress in this challenge, you can subscribe here.
If you are interested in using Apocode, sign up here.
If you want to provide feedback, discuss the idea further or get involved, email me at nicolas.tresegnie@gmail.com

Alex Mathers
3 years ago
12 habits of the zenith individuals I know
Calmness is a vital life skill.
It aids communication. It boosts creativity and performance.
I've studied calm people's habits for years. Commonalities:
Have mastered the art of self-humor.
Protectors take their job seriously, draining the room's energy.
They are fixated on positive pursuits like making cool things, building a strong physique, and having fun with others rather than on depressing influences like the news and gossip.
Every day, spend at least 20 minutes moving, whether it's walking, yoga, or lifting weights.
Discover ways to take pleasure in life's challenges.
Since perspective is malleable, they change their view.
Set your own needs first.
Stressed people neglect themselves and wonder why they struggle.
Prioritize self-care.
Don't ruin your life to please others.
Make something.
Calm people create more than react.
They love creating beautiful things—paintings, children, relationships, and projects.
Don’t hold their breath.
If you're stressed or angry, you may be surprised how much time you spend holding your breath and tightening your belly.
Release, breathe, and relax to find calm.
Stopped rushing.
Rushing is disadvantageous.
Calm people handle life better.
Are aware of their own dietary requirements.
They avoid junk food and eat foods that keep them healthy, happy, and calm.
Don’t take anything personally.
Stressed people control everything.
Self-conscious.
Calm people put others and their work first.
Keep their surroundings neat.
Maintaining an uplifting and clutter-free environment daily calms the mind.
Minimise negative people.
Calm people are ruthless with their boundaries and avoid negative and drama-prone people.

Zuzanna Sieja
3 years ago
In 2022, each data scientist needs to read these 11 books.
Non-technical talents can benefit data scientists in addition to statistics and programming.
As our article 5 Most In-Demand Skills for Data Scientists shows, being business-minded is useful. How can you get such a diverse skill set? We've compiled a list of helpful resources.
Data science, data analysis, programming, and business are covered. Even a few of these books will make you a better data scientist.
Ready? Let’s dive in.
Best books for data scientists
1. The Black Swan
Author: Nassim Taleb
First, a less obvious title. Nassim Nicholas Taleb's seminal series examines uncertainty, probability, risk, and decision-making.
Three characteristics define a black swan event:
It is erratic.
It has a significant impact.
Many times, people try to come up with an explanation that makes it seem more predictable than it actually was.
People formerly believed all swans were white because they'd never seen otherwise. A black swan in Australia shattered their belief.
Taleb uses this incident to illustrate how human thinking mistakes affect decision-making. The book teaches readers to be aware of unpredictability in the ever-changing IT business.
Try multiple tactics and models because you may find the answer.
2. High Output Management
Author: Andrew Grove
Intel's former chairman and CEO provides his insights on developing a global firm in this business book. We think Grove would choose “management” to describe the talent needed to start and run a business.
That's a skill for CEOs, techies, and data scientists. Grove writes on developing productive teams, motivation, real-life business scenarios, and revolutionizing work.
Five lessons:
Every action is a procedure.
Meetings are a medium of work
Manage short-term goals in accordance with long-term strategies.
Mission-oriented teams accelerate while functional teams increase leverage.
Utilize performance evaluations to enhance output.
So — if the above captures your imagination, it’s well worth getting stuck in.
3. The Hard Thing About Hard Things: Building a Business When There Are No Easy Answers
Author: Ben Horowitz
Few realize how difficult it is to run a business, even though many see it as a tremendous opportunity.
Business schools don't teach managers how to handle the toughest difficulties; they're usually on their own. So Ben Horowitz wrote this book.
It gives tips on creating and maintaining a new firm and analyzes the hurdles CEOs face.
Find suggestions on:
create software
Run a business.
Promote a product
Obtain resources
Smart investment
oversee daily operations
This book will help you cope with tough times.
4. Obviously Awesome: How to Nail Product Positioning
Author: April Dunford
Your job as a data scientist is a product. You should be able to sell what you do to clients. Even if your product is great, you must convince them.
How to? April Dunford's advice: Her book explains how to connect with customers by making your offering seem like a secret sauce.
You'll learn:
Select the ideal market for your products.
Connect an audience to the value of your goods right away.
Take use of three positioning philosophies.
Utilize market trends to aid purchasers
5. The Mom test
Author: Rob Fitzpatrick
The Mom Test improves communication. Client conversations are rarely predictable. The book emphasizes one of the most important communication rules: enquire about specific prior behaviors.
Both ways work. If a client has suggestions or demands, listen carefully and ensure everyone understands. The book is packed with client-speaking tips.
6. Introduction to Machine Learning with Python: A Guide for Data Scientists
Authors: Andreas C. Müller, Sarah Guido
Now, technical documents.
This book is for Python-savvy data scientists who wish to learn machine learning. Authors explain how to use algorithms instead of math theory.
Their technique is ideal for developers who wish to study machine learning basics and use cases. Sci-kit-learn, NumPy, SciPy, pandas, and Jupyter Notebook are covered beyond Python.
If you know machine learning or artificial neural networks, skip this.
7. Python Data Science Handbook: Essential Tools for Working with Data
Author: Jake VanderPlas
Data work isn't easy. Data manipulation, transformation, cleansing, and visualization must be exact.
Python is a popular tool. The Python Data Science Handbook explains everything. The book describes how to utilize Pandas, Numpy, Matplotlib, Scikit-Learn, and Jupyter for beginners.
The only thing missing is a way to apply your learnings.
8. Python for Data Analysis: Data Wrangling with Pandas, NumPy, and IPython
Author: Wes McKinney
The author leads you through manipulating, processing, cleaning, and analyzing Python datasets using NumPy, Pandas, and IPython.
The book's realistic case studies make it a great resource for Python or scientific computing beginners. Once accomplished, you'll uncover online analytics, finance, social science, and economics solutions.
9. Data Science from Scratch
Author: Joel Grus
Here's a title for data scientists with Python, stats, maths, and algebra skills (alongside a grasp of algorithms and machine learning). You'll learn data science's essential libraries, frameworks, modules, and toolkits.
The author works through all the key principles, providing you with the practical abilities to develop simple code. The book is appropriate for intermediate programmers interested in data science and machine learning.
Not that prior knowledge is required. The writing style matches all experience levels, but understanding will help you absorb more.
10. Machine Learning Yearning
Author: Andrew Ng
Andrew Ng is a machine learning expert. Co-founded and teaches at Stanford. This free book shows you how to structure an ML project, including recognizing mistakes and building in complex contexts.
The book delivers knowledge and teaches how to apply it, so you'll know how to:
Determine the optimal course of action for your ML project.
Create software that is more effective than people.
Recognize when to use end-to-end, transfer, and multi-task learning, and how to do so.
Identifying machine learning system flaws
Ng writes easy-to-read books. No rigorous math theory; just a terrific approach to understanding how to make technical machine learning decisions.
11. Deep Learning with PyTorch Step-by-Step
Author: Daniel Voigt Godoy
The last title is also the most recent. The book was revised on 23 January 2022 to discuss Deep Learning and PyTorch, a Python coding tool.
It comprises four parts:
Fundamentals (gradient descent, training linear and logistic regressions in PyTorch)
Machine Learning (deeper models and activation functions, convolutions, transfer learning, initialization schemes)
Sequences (RNN, GRU, LSTM, seq2seq models, attention, self-attention, transformers)
Automatic Language Recognition (tokenization, embeddings, contextual word embeddings, ELMo, BERT, GPT-2)
We admire the book's readability. The author avoids difficult mathematical concepts, making the material feel like a conversation.
Is every data scientist a humanist?
Even as a technological professional, you can't escape human interaction, especially with clients.
We hope these books will help you develop interpersonal skills.
