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order_id | customer_id | product | price
1        | 101         | Laptop  | 60000
2        | 102         | Phone   | 30000
3        | 101         | Mouse   | 1000

To retrieve order details:

SELECT
    order_id,
    customer_id,
    product,
    price
FROM orders;

To calculate price after adding a hypothetical 10% increase:

SELECT
    product,
    price,
    price * 1.10 AS increased_price
FROM orders;

🔹 21. SELECT in Real-World Data Science

SQL is often the first step in a Data Science workflow.

For example:

Business Question

"Give me all customer transactions from the sales database."

You might start with:

SELECT
    customer_id,
    order_date,
    product_id,
    amount
FROM transactions;

Then later:

WHERE → Filter data

GROUP BY → Aggregate data

JOIN → Combine tables

ORDER BY → Sort results

Window Functions → Advanced analysis

Eventually, you may load the SQL result into Pandas:

import pandas as pd
df = pd.read_sql(query, connection)

So SQL and Python often work together.

🔹 22. Common Beginner Mistakes

❌ Mistake 1: Forgetting the FROM clause

Incorrect:

SELECT name;

when you intend to retrieve a column from a table.

Correct:

SELECT name
FROM customers;

❌ Mistake 2: Using commas incorrectly

Correct:

SELECT name, city, age
FROM customers;

❌ Mistake 3: Confusing column names and values

A column:

city

is different from a text value:

'Pune'

We'll explore this more when we learn WHERE.

❌ Mistake 4: Using SELECT * everywhere

SELECT * is useful while learning and exploring, but for production queries, selecting only the required columns can be more efficient and clearer.

🔹 23. Interview Questions

💡 What does SELECT do?

SELECT specifies the columns or expressions that should appear in the query result.

💡 What does SELECT * mean?

It selects all columns from the specified table.

💡 What is an alias?

An alias gives a temporary name to a column or expression in the query result.

💡 What does DISTINCT do?

It removes duplicate rows from the selected result.

🎯 Practice Questions

Q1. Write a query to select all columns from a table called employees.

Q2. Write a query to select only employee_id and salary from employees.

Q3. Write a query to display salary as monthly_salary.

Q4. Write a query to calculate price * quantity as total_amount from an orders table.

Q5. Write a query to return unique values from the department column of an employees table.

🎯 Key Takeaways

✅ SQL is used to communicate with relational databases.

✅ SELECT specifies what you want to retrieve.

✅ FROM specifies the table.

✅ * means all columns.

✅ You can select one or multiple columns.

✅ AS creates a temporary alias.

✅ SQL can perform calculations.

✅ DISTINCT returns unique results.

✅ SQL is one of the most important tools for extracting data before analysis and Machine Learning.

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you tell the database:

What data you want

You generally don't tell the database exactly how to retrieve it internally.

The database's query optimizer determines an efficient execution strategy.

This is one reason SQL is called a declarative language.

🔹 11. SQL Keywords

SQL uses keywords such as:

SELECT

FROM

WHERE

GROUP BY

ORDER BY

HAVING

JOIN

These keywords define the structure of the query.

For example:

SELECT name
FROM customers;

Here:

SELECT → What to retrieve

FROM → Where to retrieve it from

🔹 12. SQL Case Sensitivity

SQL keywords are commonly written in uppercase:

SELECT

FROM

WHERE

This improves readability.

For example:

SELECT customer_id, name
FROM customers;

is easier to read than:

select customer_id,name from customers;

Most SQL database systems treat keywords as case-insensitive, although behavior regarding identifiers such as table and column names can vary by database system and configuration.

Recommended style:

Use:

UPPERCASE for SQL keywords

lowercase or snake_case for column/table names

🔹 13. Column Aliases

You can temporarily give a column a different name using AS.

Example:

SELECT
    name AS customer_name
FROM customers;

The result will display:

customer_name
Alice
Bob
Carol

The original column name in the database is not changed.

The alias only changes how the result is displayed.

🔹 14. Aliases Without AS

In many SQL systems, you can also write:

SELECT
    name customer_name
FROM customers;

However, using AS is generally clearer:

SELECT
    name AS customer_name
FROM customers;

🔹 15. Calculations in SELECT

SQL can perform calculations.

Suppose we have:

price

quantity

We can calculate total sales:

SELECT
    price,
    quantity,
    price * quantity AS total_amount
FROM orders;

This creates a calculated column:

total_amount = price × quantity

This ability becomes extremely useful in Data Analytics.

🔹 16. Using SELECT with Expressions

You can perform various calculations.

Example:

SELECT
    salary,
    salary * 12 AS annual_salary
FROM employees;

If monthly salary is:

₹50,000

then:

annual_salary = ₹600,000

The original database isn't modified.

The calculation is performed when the query runs.

🔹 17. Selecting Constants

SQL can also return constant values.

Example:

SELECT
    'Data Science' AS course;

Result:

course
Data Science

You can also use numbers:

SELECT
    2026 AS year;

Result:

year
2026

This becomes useful when constructing analytical datasets.

🔹 18. DISTINCT

DISTINCT is part of the roadmap and we'll study it properly later.

For now, understand its basic purpose:

It returns unique values.

Suppose:

city

Pune

Mumbai

Pune

Delhi

Mumbai

Query:

SELECT DISTINCT city
FROM customers;

Result:

Pune
Mumbai
Delhi

Duplicate values are removed from the result.

🔹 19. SELECT DISTINCT on Multiple Columns

You can use multiple columns:

SELECT DISTINCT city, department
FROM employees;

Important:

DISTINCT applies to the combination of selected columns.

So if two rows have the same city but different departments, they are considered different combinations.

🔹 20. SQL Query Example

Imagine an orders table:

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📍 Phase 3: SQL for Data Science

📖 Topic 1: SQL Basics — SELECT

SQL is one of the most important skills for a Data Scientist because real-world data is often stored in relational databases.

Before using Python, Machine Learning, or advanced analytics, you will frequently need to:

Retrieve data

Filter data

Combine tables

Aggregate information

Create datasets for analysis

Answer business questions

We'll start from the foundation: SELECT.

🔹 1. What Is SQL?

SQL stands for:

Structured Query Language

It is used to communicate with relational databases.

For example, a company might store:

Customers

customer_id | name  | city   | age
101         | Alice | Mumbai | 28
102         | Bob   | Pune   | 32
103         | Carol | Delhi  | 25

You can use SQL to retrieve specific information from this table.

🔹 2. What Is a Database?

A database is a structured system used to store and manage data.

A relational database stores information in tables.

For example:

Customers

Contains customer information.

Orders

Contains order information.

Products

Contains product information.

These tables can be related using common columns such as:

customer_id

This becomes extremely important when we learn JOINs.

🔹 3. What Is a Table?

A table consists of:

Rows

Each row generally represents one record.

Example: One customer

Columns

Each column represents an attribute.

Example: customer_id, name, city, age

So:

Row → Record

Column → Attribute

🔹 4. Your First SQL Query

The basic SQL query is:

SELECT *
FROM customers;

Let's break it down:

SELECT

Specifies what data you want.

*

Means: Select all columns.

FROM

Specifies the table from which you want the data.

customers

The table name.

So the query means:

Give me all columns from the customers table.

🔹 5. Selecting Specific Columns

You don't always need every column.

Suppose you only want:

Customer ID

Customer name

Use:

SELECT customer_id, name
FROM customers;

Result:

customer_id | name
101         | Alice
102         | Bob
103         | Carol

This is usually better than using SELECT * when you only need a few columns.

🔹 6. Selecting One Column

You can select a single column:

SELECT name
FROM customers;

Result:

name
Alice
Bob
Carol

🔹 7. Selecting Multiple Columns

Separate column names using commas:

SELECT name, city, age
FROM customers;

This returns only those three columns.

🔹 8. What Does * Mean?

The asterisk:

*

means: All columns.

Example:

SELECT *
FROM customers;

If the table has 10 columns, the query returns all 10.

However, in production environments, it is often better to explicitly specify the columns you need.

Instead of:

SELECT *
FROM customers;

prefer:

SELECT customer_id, name, city
FROM customers;

when those are the only fields required.

🔹 9. SQL Statements and Semicolon

SQL statements are commonly terminated with:

;

Example:

SELECT name
FROM customers;

The semicolon indicates the end of the SQL statement in many SQL environments.

🔹 10. SQL Is Declarative

This is an important concept.

When you write:

SELECT name
FROM customers;

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The posterior mean is: 9 / (9 + 5) = 9 / 14 ≈ 0.643

🔹 24. Common Mistakes

❌ Mistake 1: Thinking the prior is always subjective - A prior can come from historical data, previous studies, domain knowledge.

❌ Mistake 2: Confusing likelihood with posterior - Likelihood = P(Data | Parameter), Posterior = P(Parameter | Data). They are not the same.

❌ Mistake 3: Ignoring the base rate - The prior probability can have a major impact, especially when an event is rare.

❌ Mistake 4: Confusing confidence intervals with credible intervals - They have different statistical interpretations.

❌ Mistake 5: Thinking Bayesian methods ignore data - They don't. Bayesian inference combines prior information with observed evidence.

🔹 25. Interview Perspective

💡 What is Bayesian Statistics?

Bayesian Statistics is an approach to statistical inference that combines prior information with observed data to produce a posterior distribution representing updated beliefs about unknown parameters.

💡 What are Prior, Likelihood and Posterior?

Prior represents information before observing the new data, likelihood describes how compatible the observed data is with different parameter values, and posterior represents the updated distribution after combining the prior and likelihood.

💡 MLE vs MAP?

MLE estimates parameters using only the likelihood, while MAP combines the likelihood with a prior distribution.

🎯 Practice Questions

Q1. What are the three main components of Bayesian inference?

Q2. What is the difference between prior and posterior probability?

Q3. What is the difference between MLE and MAP?

Q4. Why is the base rate important in Bayesian reasoning?

Q5. What is the main difference between a confidence interval and a credible interval?

🎯 Key Takeaways

✅ Bayesian Statistics = Prior + Data → Posterior

✅ Prior = Belief/information before observing new data.

✅ Likelihood = How compatible the observed data is with different parameter values.

✅ Posterior = Updated belief after considering the data.

✅ Posterior ∝ Prior × Likelihood

✅ MLE uses likelihood.

✅ MAP uses prior + likelihood.

✅ Bayesian methods naturally represent uncertainty using probability distributions.

✅ Naive Bayes is a major Machine Learning algorithm based on Bayes' theorem.

✅ Bayesian inference is especially useful when information arrives sequentially and beliefs need to be updated.

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New evidence: A machine starts producing unusual measurements. The likelihood of seeing those measurements may be much higher when a machine is faulty.

Updated belief: After combining the historical information and new evidence, the probability that the machine is faulty increases. If additional sensor data arrives, the estimate can be updated again.

This makes Bayesian methods particularly useful for continuous monitoring and decision systems.

🔹 21. Advantages of Bayesian Statistics

✅ 1. Incorporates Prior Knowledge - Previous research or historical information can be included.

✅ 2. Naturally Represents Uncertainty - Posterior distributions provide a full representation of uncertainty.

✅ 3. Supports Continuous Updating - New data can update previous beliefs.

✅ 4. Useful with Limited Data - A carefully chosen prior can provide useful information when data is limited.

✅ 5. Powerful for Complex Models - Bayesian methods can be extended to sophisticated hierarchical and probabilistic models.

🔹 22. Limitations

❌ 1. Choosing a Prior Can Be Difficult - Different priors can sometimes lead to different results, especially when data is limited.

❌ 2. Computationally Expensive - Complex Bayesian models may require substantial computation.

❌ 3. Requires Careful Modeling - An inappropriate likelihood or prior can produce misleading results.

❌ 4. Can Be More Complex - Bayesian modeling may require more mathematical and computational knowledge.

🔹 23. Python Example

A simple Bayesian calculation can be illustrated using a Beta prior for a Bernoulli probability.

Suppose: Prior = Beta(2, 2). We observe: 7 successes and 3 failures. The posterior becomes: Posterior = Beta(2 + 7, 2 + 3) = Beta(9, 5)

Python:

from scipy.stats import beta

alpha_prior = 2
beta_prior = 2

successes = 7
failures = 3

alpha_posterior = alpha_prior + successes
beta_posterior = beta_prior + failures

posterior_mean = alpha_posterior / (alpha_posterior + beta_posterior)
print("Posterior Mean:", posterior_mean)

For example: A 95% credible interval represents a range containing 95% of the posterior probability for the parameter, given the model, prior, and observed data. This is a major conceptual difference.

🔹 14. Bayesian Example: Coin

Suppose we have a coin and want to estimate its probability of producing Heads. Before collecting data, we might believe the coin is probably close to fair. That's our prior. Then we observe: 8 Heads out of 10 tosses. This is the data. The likelihood tells us how compatible those observations are with different values of the coin's probability. We then combine the prior and likelihood to obtain a posterior distribution.

🔹 15. Why Use a Distribution Instead of One Number?

In Bayesian statistics, we're often interested in a posterior distribution rather than just a single estimate.

Suppose we want to estimate: Probability of customer purchase. Instead of saying: p = 0.65, we might obtain a distribution showing that some values are more plausible than others. For example, values around 0.60–0.70 might have high posterior probability. This allows us to represent uncertainty more explicitly.

🔹 16. Bayesian Estimation

Bayesian estimation uses the posterior distribution to estimate unknown parameters.

Common summaries include:

• Posterior Mean: Average value of the posterior distribution.

• Posterior Median: Middle value of the posterior distribution.

• MAP Estimate: Maximum A Posteriori estimate. This is the parameter value with the highest posterior density. MAP is related to MLE.

🔹 17. MLE vs MAP

Maximum Likelihood Estimation: Uses Likelihood. MLE chooses the parameter that maximizes: P(Data | Parameter)

Maximum A Posteriori: Uses Prior + Likelihood. MAP chooses the parameter that maximizes: P(Parameter | Data)

In simplified form: MLE → Likelihood, MAP → Prior + Likelihood. If the prior is uniform over the relevant parameter space, MAP and MLE can coincide.

🔹 18. Bayesian Statistics in Machine Learning

📨 Spam Detection - Estimate the probability that an email is spam based on its features.

🏥 Medical Diagnosis - Update disease probabilities based on symptoms and test results.

🛒 Recommendation Systems - Update beliefs about user preferences based on interactions.

💳 Risk Modeling - Update risk estimates as new customer information becomes available.

🤖 Bayesian Networks - Represent probabilistic relationships between variables.

🧠 Natural Language Processing - Bayesian approaches can be used in probabilistic language models and classification.

🔹 19. Naive Bayes

One of the most famous Machine Learning algorithms based on Bayes' theorem is: Naive Bayes

It is commonly used for: Spam classification, Text classification, Sentiment analysis, Document classification

The "naive" assumption is that features are conditionally independent given the class. For example, in spam classification, the model may consider words such as: "free", "offer", "winner" and estimate the probability that an email belongs to the spam class.

🔹 20. Bayesian Updating in Real Life

Imagine you're trying to determine whether a machine in a factory is malfunctioning.

Initial belief: Historical data suggests 5% of machines have a problem. This is your prior.

Suppose a disease affects 1% of a population.

So: P(Disease) = 0.01.

A medical test is positive for someone who has the disease 99% of the time. But the test can also be positive for healthy people.

Suppose: P(Positive | No Disease) = 5%

Now someone receives a positive test. The important question is:

What is the probability that this person actually has the disease?

This is not simply 99%. We need to consider: The prior probability of the disease, The probability of a positive test among people with the disease, The probability of a positive test among people without the disease. Bayes' theorem combines these pieces of information.

🔹 8. Solving the Example

Let's assume:

P(Disease) = 0.01

P(Positive | Disease) = 0.99

P(No Disease) = 0.99

P(Positive | No Disease) = 0.05

First calculate the overall probability of a positive test:

P(Positive) = (0.99 × 0.01) + (0.05 × 0.99) = 0.0099 + 0.0495 = 0.0594

Now: P(Disease | Positive) = (0.99 × 0.01) / 0.0594 ≈ 0.167

So the probability is approximately 16.7%. This is much lower than 99%.

Because the disease is relatively rare and false positives occur. This demonstrates why base rates matter.

🔹 9. Base Rate

The base rate is the underlying frequency of an event in the population. In the previous example: Disease prevalence = 1%. That's the base rate.

Ignoring the base rate can lead to incorrect conclusions. This is known as the Base Rate Fallacy. A test can be highly accurate while the probability that a randomly selected person with a positive result actually has the disease can still be considerably lower than expected if the condition is rare.

🔹 10. Bayesian Updating

One of the most useful ideas in Bayesian Statistics is updating.

Suppose we initially believe: Probability of an event = 20%. Then we observe strong evidence supporting the event. Our posterior might become: 45%. Then we receive additional evidence. The probability might update again: 65%.

The process continues as new evidence arrives. So Bayesian inference is naturally suited to situations where:

New information arrives continuously.

🔹 11. Prior, Likelihood and Posterior

A simple way to remember the three:

🟦 Prior - What did I believe before seeing the data?

🟨 Likelihood - How strongly does the observed data support different possibilities?

🟩 Posterior - What do I believe after considering the data?

Remember: Posterior ∝ Prior × Likelihood

🔹 12. Bayesian vs Frequentist Statistics

Frequentist Approach: Generally treats unknown parameters as fixed but unknown. Probability is associated with the behavior of random data and procedures. Examples include: p-values, Confidence intervals, Hypothesis testing

Bayesian Approach: Treats uncertainty about parameters using probability distributions. It combines: Prior information + Data → Posterior. Examples include: Posterior distributions, Credible intervals, Bayesian parameter estimation

🔹 13. Confidence Interval vs Credible Interval

Confidence Interval: A frequentist concept. A 95% confidence interval is interpreted through the long-run behavior of the procedure that generates the interval.

Credible Interval: A Bayesian concept.

🚀 Data Science Roadmap 2026

📘 Phase 2: Mathematics & Statistics for Data Science

📖 Topic 16: Bayesian Statistics — Prior, Likelihood & Posterior

Bayesian Statistics is an important approach to statistical inference.

It provides a framework for updating our beliefs about an unknown quantity when new evidence becomes available.

The central idea is:

Start with prior information, observe new data, and update your belief to obtain a posterior distribution.

Bayesian methods are widely used in: Machine Learning, Classification, Medical diagnosis, Spam detection, Risk analysis, Recommendation systems, A/B testing, Natural Language Processing.

🔹 1. What Is Bayesian Statistics?

Suppose a company wants to determine whether a customer is likely to purchase a product.

Before seeing any new information, we may already have some historical knowledge about the customer's purchase probability.

Then we observe new information: Previous purchases, Website activity, Product views, Time spent on the website.

We can combine the previous information with the new evidence. This produces an updated belief. That is the basic idea of Bayesian Statistics.

🔹 2. Bayes' Theorem

Bayesian inference is based on Bayes' Theorem.

The simple form is:

P(A | B) = [P(B | A) × P(A)] / P(B)

Where:

P(A | B) = Probability of A given B

P(B | A) = Probability of B given A

P(A) = Prior probability of A

P(B) = Probability of observing B

In Bayesian terminology:

Posterior ∝ Likelihood × Prior

This is one of the most important relationships to remember.

🔹 3. Prior Probability

The prior represents our initial belief about a parameter or hypothesis before observing the new data.

For example: Suppose historical data shows that approximately 10% of customers purchase a particular product. Before analyzing today's customer behavior, we might use: Prior probability = 10%

The prior can come from: Historical data, Previous experiments, Domain knowledge, Earlier studies, Expert knowledge

🔹 4. Likelihood

The likelihood tells us how compatible the observed data is with a particular hypothesis or parameter value.

Suppose we observe that a customer: Visited the product page 10 times, Added the product to the cart, Returned to the website multiple times

We can ask:

How likely is this behavior if the customer is actually going to purchase?

This information contributes to the likelihood.

🔹 5. Posterior Probability

The posterior is our updated belief after considering the observed data.

In simple terms: Prior + Evidence → Posterior

For example: Before observing new behavior: Purchase probability = 10%. After observing strong purchase-related behavior: Updated probability = 35%. The 35% represents our updated belief based on the evidence and prior information.

🔹 6. The Bayesian Process

Bayesian inference can be thought of as a cycle:

Step 1: Start with a Prior - What did we believe before seeing the new data?

Step 2: Collect Data - Observe new evidence.

Step 3: Calculate Likelihood - How compatible is the evidence with different possibilities?

Step 4: Update - Combine prior and likelihood.

Step 5: Obtain Posterior - The posterior becomes our updated belief.

🔹 7. Simple Example: Medical Testing

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➊ Understand What AI Agents Are → Autonomous systems that can perceive, reason, and act
↓
➋ Master the Basics → Python, Data Structures, APIs, and JSON handling
↓
➌ Explore LLMs as Agents → Understand how GPT, Claude, or Gemini can act as reasoning agents
↓
➍ Tool Use & Function Calling → Learn how agents use tools, call APIs, and perform tasks dynamically
↓
➎ Agent Frameworks →
LangChain: For chaining LLM calls and memory
AutoGen / Autogen Studio: For multi-agent collaboration
Haystack: For document question answering
↓
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↓
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🔥 SQL Interview Case Studies & Real-World Business Problems

🧠 Case Study 1: Top 3 Customers by Revenue
📊 Orders Table
order_id customer_id amount
1 101 500
2 102 1000
3 101 700

❓ Business Question
Find the top 3 customers by total revenue.

✅ Solution
SELECT customer_id,
SUM(amount) AS total_revenue
FROM orders
GROUP BY customer_id
ORDER BY total_revenue DESC
LIMIT 3;

🧠 Case Study 2: Department with Highest Average Salary

❓ Business Question
Which department has the highest average salary?

✅ Solution
SELECT department,
AVG(salary) AS avg_salary
FROM employees
GROUP BY department
ORDER BY avg_salary DESC
LIMIT 1;

🧠 Case Study 3: Customers Who Never Ordered
📊 Tables
Customers customer_id name
Orders order_id customer_id

❓ Business Question
Find customers who never placed an order.

✅ Solution
SELECT c.customer_id,
c.name
FROM customers c
LEFT JOIN orders o
ON c.customer_id = o.customer_id
WHERE o.customer_id IS NULL;

🧠 Case Study 4: Second Highest Salary

❓ Business Question
Find employees with the second highest salary.

✅ Solution
SELECT *
FROM employees
WHERE salary = (
SELECT MAX(salary)
FROM employees
WHERE salary < (
SELECT MAX(salary)
FROM employees
)
);

🧠 Case Study 5: Monthly Sales Trend

❓ Business Question
Calculate monthly sales.

✅ Solution
SELECT YEAR(order_date) AS year,
MONTH(order_date) AS month,
SUM(amount) AS sales
FROM orders
GROUP BY YEAR(order_date),
MONTH(order_date)
ORDER BY year, month;

🎯 Practice Tasks
1️⃣ Find top-selling product
2️⃣ Find employee with highest salary in each department
3️⃣ Find customers with more than 5 orders
4️⃣ Find month with highest sales
5️⃣ Find departments having more than 10 employees

⚡ Mini Challenge 🔥
E-commerce Scenario

Tables:
Customers customer_id name
Orders order_id customer_id amount order_date

Business Question
Find the top 5 customers by total spending in the last 12 months.

🔥 Interview Tip
Most SQL interviews are NOT about syntax.

They're about:
✅ Understanding business problem
✅ Choosing the right approach
✅ Writing efficient SQL

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GigaChat 3.5 Reasoning is a new open-source LLM designed to reason before generating responses. The model breaks problems into stages, builds execution plans, checks intermediate results, and self-corrects when needed.

Built on GigaChat 3.5 Ultra, it was trained on math and coding tasks using multiple step-by-step reasoning paths. An automated verification step reinforces the paths that lead to correct answers, enabling the model to plan multi-step actions, decide when to call external tools, and revise earlier steps independently.

The model uses a proprietary linear attention architecture, which improves efficiency on long contexts by retaining key processed points rather than re-matching queries against the entire prior text.

On math problems, GigaChat 3.5 Reasoning uses on average 37% fewer tokens than DeepSeek V4 Flash Preview. Benchmark gains over the non-reasoning version:
• IFBench: 44 → 77
• Natural Plan: 64 → 80
• LiveCodeBench v6: 56 → 85

The model is open-sourced under the MIT license. Weights are available on Hugging Face:  fp8 | bf16

𝗧𝗼𝗽 𝟭𝟱 𝗣𝘆𝘁𝗵𝗼𝗻 𝗜𝗻𝘁𝗲𝗿𝘃𝗶𝗲𝘄 𝗤𝘂𝗲𝘀𝘁𝗶𝗼𝗻𝘀 𝗬𝗼𝘂 𝗠𝗨𝗦𝗧 𝗞𝗻𝗼𝘄! 🔥

Preparing for a Python Developer or Data Analyst interview?

Strengthen your fundamentals with these essential interview topics.

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