If you start learning machine learning in 2026, it is easy to have the illusion:

There is too much information, but too few people really know "what to learn first and what to learn later."

You may have collected a bunch of courses, downloaded several classic textbooks, and watched many videos of "Learning AI in 30 Days". But after studying for a while, I still encounter several typical problems:

• Python can write a little, but it won't really handle machine learning projects;
• Know the terms linear regression and neural network, but don't know why they are effective;
• Mathematical formulas can understand individual symbols, but do not know what the formula is doing as a whole;
• I can call PyTorch, but I don't know how to check it when I encounter a tensor shape error;
• I have trained the model with the tutorial, but will not do my own projects after leaving the tutorial;
• After completing a course, I found that I had forgotten most of the content after a few months.

The real difficulty is often not "no learning materials", butThere is a problem with the learning order。

A recent article on the learning route of machine learning published on Reddit also raised a similar point: One of the core problems of machine learning self-study is that a large amount of knowledge is pre-dependent on each other. If you skip the basics, it is easy to constantly encounter "This concept should I learn it first?" problem. The author divides the route into multiple stages based on a study commitment of about 8 to 10 hours per week.

Below, we reorganize this route into a machine learning roadmap that is more suitable for learners in 2026.

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1. The first stage: First learn Python that "it can do machine learning"

Why not learn AI directly?

The first reaction of many beginners is:

"I want to learn ChatGPT, Transformer, and Big Model."

But if the basics of Python are not good enough, when you learn PyTorch, data processing, and model training later, you will face two problems at the same time:

One is a machine learning problem and the other is a programming problem.

This will make learning more difficult times.

Therefore, the goal of the first phase is not to become a Python expert, but to:

Master enough Python to read, write, and debug machine learning code.

Focus on mastering the following:

1. Python basic syntax

Including:

• variables
• digital
• string
• boolean value
• None
• condition judgment
• cycle
• list
• tuple
• set
• dictionary

Especially dictionaries.

A large number of configurations, data structures, model parameters, and experimental results in machine learning projects use dictionaries or similar data structures.

2. function

Need to understand:

• parameters and return values
• default parameters
• *args
• **kwargs
• scope
• lambda
• type prompt

Don't be satisfied with just being able to call functions.

You should be able to see an unfamiliar function and make a rough judgment:

What data does it accept? What data is returned? When can something go wrong?

3. object-oriented

You don't need to delve into design patterns from the beginning, but at least understand:

• class
• object
• inheritance
• method
• __init__
• dataclass
• Common dunder methods

The reason is simple:

PyTorch's model uses classes heavily.

If you don't understand Python classes at all, then see nn.Module It is easy to create additional cognitive burden.

4. Document and data processing

At least master:

• file reading and writing
• pathlib
• JSON
• CSV
• Modules and imports
• virtual environment
• package management

Especially virtual environments.

When many beginners actually do a machine learning project for the first time, what they encounter is not a model problem, but:

"Why does my computer work but can't it work in another environment?"

Environmental management itself is an engineering capability.

5. Python Data Science Tool Chain

Gradually become familiar with:

• NumPy
• pandas
• scikit-learn
• PyTorch

You don't need to be a Python expert here.

Your goals should be:

You can independently read a common machine learning project and modify the code within it.

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2. Phase 2: Learning the mathematics that machine learning really needs

Mathematics is the most misunderstood part of the machine learning route.

Someone said:

"Machine learning doesn't require mathematics, just call the library directly."

Others believe that:

"You must first learn all advanced mathematics, linear algebra, and probability theory."

Both views can easily mislead beginners.

More practical goals are:

Learn mathematics that explains models, loss functions, optimization processes, and evaluation results.

The original post divides the mathematics part into mathematical symbol basics, linear algebra, calculus and optimization, probability statistics, information theory, and numerical calculation.

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1. Linear Algebra: One of the languages of machine learning

This is the most worthwhile mathematical direction to invest your time.

Need to understand:

• scalar
• vector
• matrix
• tensor
• dot product
• matrix multiplication
• transpose
• norm
• orthogonal
• projection
• eigenvalue
• feature vector
• SVD
• low rank approximation

Why is it important?

Because one of the most basic calculations of neural networks is:

Matrix multiplication + nonlinear function.

For example:

y = Wx + b

If you truly understand the W、x、b What they represent, we have begun to understand the internal structure of the neural network.

Rather than treating the neural network as a mysterious black box.

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3. Calculus and Optimization: Understanding "Why Models Learn"

The training process in machine learning is essentially looking for:

How to modify the parameters to make the loss function smaller?

This requires calculus and optimization.

Highlights include:

• derivative
• partial derivative
• gradient
• Jacobian
• Hessian
• chain rule
• Taylor expansion
• convex function
• local minimum
• saddle point
• automatic differentiation
• backpropagation

The most important concepts are:

Gradient, chain rule, back propagation.

If you understand:

loss
 ↓
gradient
 ↓
parameter update

Then you begin to understand what "training a neural network" means.

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4. Probability and Statistics: Understanding Uncertainty in Data and Models

Machine learning is not just about matrix operations.

The data faced by the model is inherently uncertain.

Therefore, it is necessary to understand:

• random variables
• probability distribution
• conditional probability
• joint probability
• marginal probability
• Bayes 'theorem
• desired
• variance
• covariance
• normal distribution
• maximum likelihood estimation
• MAP
• confidence interval
• hypothesis testing
• Bootstrap

In particular, you need to understand:

The loss function is often related to some probability assumption.

For example, there is a link between mean square error and Gaussian noise assumptions, and cross-entropy in classification tasks can also be understood from a probability modeling perspective.

When you understand this,"Why does this task use this loss" is no longer just memorizing the formula.

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5. Information theory and numerical calculations: Don't ignore these "little knowledge"

It often appears in machine learning:

• Entropy
• Cross-Entropy
• KL Divergence
• Mutual Information

These concepts are very common in modern deep learning.

For example, why do classification models often use cross-entropy?

If you understand entropy, probability distributions, and maximum likelihood, you can understand it in principle rather than rote:

"Classification = Cross Entropy."

At the same time, you should also understand some numerical calculation issues:

• floating point
• overflow
• underflow
• NaN
• log-sum-exp
• numerical stability

Because when training models in real life, it often appears:

loss = NaN

At this time, it is not enough to just know the "gradient descent".

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6. Phase 3: Learn PyTorch, but learn Tensor first

Many people learn PyTorch by:

Find a CNN tutorial → Copy the code → Run.

This method can get you a quick result, but it may not allow you to truly understand PyTorch.

A better approach is to understand Tensor first.

Key points:

• What is Tensor?
• shape
• dtype
• device
• reshape
• indexing
• broadcasting
• matrix multiplication
• reduction
• View and copy
• autograd
• Conversion between NumPy and PyTorch
• GPU / CPU
• Random Numbers and Reproducibility

especially shape。

For example:

(batch, sequence, features)

You should be able to explain immediately:

• What is a batch?
• What is sequence?
• What are features?
• If the dimensions are changed, will the model still accept it?

Many deep learning bugs are not essentially "algorithms can't", but:

Tensor's shape is wrong.

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7. Phase 4: Really enter the foundation of machine learning

Here, we begin to enter the core of machine learning.

This stage can be divided into five parts.

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Part 1: Start with a neuron

First understand:

• What is a model
• What are parameters
• What is loss
• What is an optimizer
• supervised learning
• unsupervised learning
• semi-supervised learning
• self-supervised learning
• reinforcement learning

Then start with the simplest model:

linear regression

You need to understand:

How does the model generate predictions based on input?

Then learn:

• MSE
• MAE
• RMSE
• Huber Loss

Then enter the categories:

• Sigmoid
• Logistic Regression
• Binary Cross Entropy
• Softmax
• Multiclass Classification
• Multilabel Classification

This step is very important.

Because it establishes a framework that runs through the entire deep learning:

数据
 ↓
模型
 ↓
预测
 ↓
Loss
 ↓
Gradient
 ↓
更新参数
 ↓
重复

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8. From a neuron to a deep neural network

Next, enter:

Multilayer Perceptron, or MLP.

Understand:

• layer
• hidden layer
• width
• depth
• parameter
• hyperparameter
• activation function

Then learn:

• Step
• Sigmoid
• Tanh
• ReLU
• Leaky ReLU
• GELU

Why do I need to activate the function?

Because if each layer is just a linear transformation, no matter how many layers are stacked, they can still essentially be merged into one linear transformation.

Therefore:

Nonlinear activation functions are one of the important reasons why deep neural networks are able to learn complex functions.

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9. Training neural networks: true core competencies

Being able to write a neural network does not mean that you can train the neural network.

Next, you need to understand the optimizer.

The learning order can be:

Gradient Descent
        ↓
SGD
        ↓
Momentum
        ↓
AdaGrad
        ↓
RMSProp
        ↓
Adam
        ↓
AdamW

These require special attention:

Learning Rate

Learning rate is usually one of the very critical hyperparameters in the training process.

Too big:

loss → 爆炸

Too small:

loss → 几乎不动

So you need to understand:

• learning rate
• learning rate schedule
• warmup
• cosine decay
• step decay

Instead of simply putting:

lr=0.001

Make it the correct answer.

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10. Learn to watch the Loss Curve

This is the ability that is most easily ignored in many tutorials, but is very important in practical work.

Assumption:

Train Loss ↓
Validation Loss ↓

It usually means that training is progressing normally.

But if:

Train Loss ↓
Validation Loss ↑

You should think of:

Overfitting may have occurred.

If both are high, there may be:

• The model is too simple
• insufficient training
• eigenproblem
• Learning rate issues
• data problems

So true machine learning capabilities are not:

"I will run the training code."

Instead:

After seeing the training results, I knew what to check next.

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11. Generalization: Can models work in the real world

A high score on the training set does not mean that the model is really good.

What really matters is:

How does the model perform when faced with data it has not seen?

Therefore, it is necessary to understand:

• Generalization
• Overfitting
• Underfitting
• Bias-Variance
• Regularization
• Weight Decay
• L1
• Dropout
• Label Smoothing
• Early Stopping
• Hyperparameter Search

Also understand a very important question:

Data Leakage

If information from the test set accidentally enters the training process, the final test score may be completely meaningless.

This is why machine learning projects cannot just pursue a beautiful accuracy.

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12. Evaluation models: Don't just look at Accuracy

Different tasks require different indicators.

Classification questions can be used:

• Accuracy
• Precision
• Recall
• F1
• Confusion Matrix
• ROC-AUC
• PR-AUC
• MCC

Regression questions may use:

• MAE
• MSE
• RMSE
• R²
• MAPE

The most important question is not:

"Which indicator is the highest?"

Instead:

"Does this indicator really reflect the problem the model is trying to solve?"

For example, on datasets with severe category imbalances, simply looking at accuracy may be misleading.

Assume that 99% of the sample belongs to Category A.

The model does nothing but predicts A:

Accuracy = 99%

It looks high.

But the model may not be able to identify the truly important Class B at all.

So before evaluating a model, you must first understand:

What are the business goals?

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13. In addition to models, we must also learn engineering indicators

In the real environment, a model does not just look at accuracy.

Also need to consider:

• parameter quantity
• model size
• FLOPs
• latency
• throughput
• memory
• reasoning cost
• deployment environment

A model with a slightly higher accuracy may not be suitable for practical application if the reasoning cost is tens of times higher.

So machine learning will eventually start from:

"Can the model work?"

Gradually moving towards:

"Can models work stably, quickly and at low cost?"

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14. Stage 5: Choose your own direction

After completing the basics of machine learning, don't continue to learn "all AI" without restrictions.

Because at this stage, the domain will quickly branch.

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Direction 1: Natural Language Processing NLP

You can continue to learn:

• Tokenization
• Embedding
• Language Modeling
• Attention
• Transformer
• Fine-tuning
• Retrieval
• LLM
• Evaluation

If you want to move further into generative AI, this route can be very important.

---

Direction 2: Computer vision

You can learn:

• Image Processing
• CNN
• Representation Learning
• Object Detection
• Image Segmentation
• Vision Transformer
• Multimodal Models

---

Direction 3: Strengthen learning

Continue learning:

• Markov Decision Process
• Value Function
• Policy
• Q-Learning
• Policy Gradient
• Actor-Critic
• Deep Reinforcement Learning

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Direction 4: AI Agent and application-based AI

AI learning in 2026 can further enter:

• Tool Calling
• RAG
• Agent Architecture
• Workflow
• Memory
• Evaluation
• Multi-Agent Systems
• AI Application Engineering

But here is a key principle:

Don't completely skip the basics of machine learning just because popular concepts such as Agent and LLM emerge.

If your goal is to do AI applications, you certainly don't need to learn all mathematics at the researcher level.

But if your goal is to understand models, train models, debug models, or even conduct research, the importance of basic knowledge remains.

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15. The question that is really easy to ignore: How can I not forget it after learning?

This may be one of the most important issues along the entire route.

Many people have this experience:

"I obviously learned neural networks. Why can't I explain back propagation clearly now?"

Because:

Understand ≠ master.

When watching the video, you feel:

"Yeah, I understand."

But after a few weeks, you may only have a vague impression.

The truly effective method is:

1. doing the problem

Don't just look at code questions.

Concept questions are equally important.

For example, after learning gradient descent, try to answer:

What happens if the learning rate increases?

Why might the gradient disappear?

Why does Adam behave differently from SGD?

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2. Interval review

Don't study for 10 hours a day and then stay away for a month.

A more effective way is to:

第一次学习
↓
几天后复习
↓
一两周后再次复习
↓
一个月后重新测试

Especially if you have answered incorrectly, you should increase the frequency of review.

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3. Important code must be written by yourself

For example:

• training loop
• loss function
• evaluation loop
• data preprocessing
• checkpoint
• metrics

Don't always rely on copy-paste.

You should at least once:

Don't read the tutorial at all and start writing from an empty file.

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16. Don't wait until you finish learning before starting working on the project

This is one of the most common pitfalls in learning machine learning.

Someone plans:

Python
↓
数学
↓
机器学习
↓
深度学习
↓
Transformer
↓
LLM
↓
终于开始做项目

The question is:

This can take a very long time.

A better approach is:

While learning the basics, we continue to work on increasingly complex projects.

For example:

Project 1: Linear Regression

Forecast house prices.

Study:

• data
• features
• loss
• gradient descent
• evaluation

Project 2: Second Classification

Predicting whether users are lost.

Study:

• logistic regression
• precision
• recall
• F1
• confusion matrix

Project 3: Image Classification

For example, CIFAR-10.

Study:

• CNN
• DataLoader
• augmentation
• training loop
• validation

Project 4: Text Classification

For example, sentiment analysis.

Study:

• tokenization
• embeddings
• sequence modeling
• Transformer

Project 5: Complete AI Applications

For example:

用户问题
   ↓
Retriever
   ↓
Relevant Documents
   ↓
LLM
   ↓
Answer
   ↓
Evaluation

At this time, what you start to come into contact with is not just the model, but the complete AI system.

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17. A more realistic study schedule for 2026

If you can invest about 8 to 10 hours a week, you can understand the entire process as a long-term project rather than a "crash course."

A reference rhythm is:

stage	focus	reference time
the first phase	Python	3~5 weeks
the second phase	mathematical basis	6~10 weeks
the third stage	PyTorch	about 2 weeks
the fourth stage	Fundamentals of ML / Deep Learning	10~14 weeks
Phase V	professional direction	continuous learning
project phase	Practical combat and collection of works	Synchronizing with learning

These times are not countdown to exams.

People with a strong foundation in mathematics can do it faster, while people with no programming experience at all may take longer. The time estimate given in the original post is also based on the premise of about 8 to 10 hours per week and the practice is actually completed.

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18. Finally: Don't turn the "learning route" into a new way of procrastination

The most dangerous learning state is not "not knowing what to learn".

Instead:

Always looking for the next course.

You may keep searching:

• The best Python courses
• The best mathematics courses
• The best ML courses
• The best PyTorch tutorials
• The best Transformer tutorials
• The best LLM courses

In the end, I collected 50 courses but did not complete a single project.

The truly effective learning path should be:

学习一个概念
      ↓
写代码
      ↓
做练习
      ↓
遇到问题
      ↓
查资料
      ↓
解决问题
      ↓
重新实现
      ↓
做项目
      ↓
复习

Instead of:

看视频
↓
看更多视频
↓
收藏课程
↓
看路线图
↓
重新寻找路线图

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Conclusion: The most important thing to learn machine learning in 2026 is not to catch up with hot spots

AI technology changes very rapidly.

Transformers are popular today, and new architectures may appear tomorrow; today everyone is discussing LLM, and new model paradigms will appear in the future.

Therefore, if you only learn a specific tool, it is easy to start over as the tool changes.

What is really worth building are lower-level capabilities:

Python → Mathematics → Tensor → Models → Optimization → Generalization → Evaluation → Engineering → Professional Directions

Eventually you should reach this state:

When you see a new model, you don't just ask:

"Are there any tutorials?"

Instead, you can ask:

• What is its input?
• What is the output?
• What are the parameters?
• What is the loss function?
• Why design this way?
• How to train?
• How to evaluate?
• Where can overfitting occur?
• What is the cost of reasoning?
• If the results are not good, where should I start checking?

When you start to be able to answer these questions yourself, you are no longer just a "person who can use machine learning tools."

You are truly building your machine learning capabilities.

Learning machine learning is not about memorizing all 350 concepts, but building a knowledge network so that every new concept you learn knows why it exists, what it relies on, and where it should play a role.

This is the most worthwhile goal for learning machine learning in 2026.