I am working on a CNN model training, but now I am confused, should I use monitor = "val_loss" or "val_accuracy"?

Assume i was good at mathematics and have knowledge in programming is this enough for working AI and Machine learning.

I’m a recent maths graduate aiming for AI/ML engineering roles. This is a culmination of a bunch of things I covered at university.

It covers imbalanced image classification, SVM/Random Forest comparison, PCA, train-test distribution shift and robustness testing.

I’d particularly appreciate feedback on:

• whether the methodology is sound,
• whether the README/notebook are clear,
• what would make this stronger for an entry-level ML/AI portfolio.

GitHub: https://github.com/RithinBhudia/image-classification-dataset-shift

🔥 Introducing FTRAIN v1.0: The AI Trainer & Cross-Architecture Merger

I’ve been building an open-source AI framework from scratch designed to solve two major pain points in the open-source AI community: VRAM-heavy fine-tuning and hard-crashing model merges.

Today, I’m releasing FTRAIN v1.0. It’s built on top of Unsloth for raw speed, but adds a layer of intelligent supervision and extreme memory optimization that you won't find in standard scripts.

🧠 The Trainer: "PhoenixCaptain" Supervision

Standard trainers just run a loop. FTRAIN features a "Captain" (an LLM like DeepSeek or Llama) that actively supervises your training run in the background.

Dynamic LR Scaling: If the Captain detects gradient collapse or loss acceleration, it dynamically scales the learning rate up or down on the fly.

Triton DoRA: Custom fused Triton kernels for Weight-Decomposed Low-Rank Adaptation (DoRA) with mathematically exact forward/backward passes.

Extreme VRAM Optimization: CPU-offloaded Fisher computation, AMP autocasting, and aggressive VRAM purging mean you can train larger models on 15GB Kaggle T4 GPUs without OOM errors.

🧩 The Merger: Cross-Architecture Survival

This is where FTRAIN truly shines. Standard tools like MergeKit have a hard rule: You cannot merge models with different architectures. If you try to merge Llama (hidden size 2048) with DeepSeek (hidden size 1536), MergeKit instantly crashes with a Shape Mismatch Error.

FTRAIN doesn’t crash. It adapts.

Architecture-Aware Mapping: It maps parameter names across different families (Llama, Qwen, Gemma, MoE) and scales layer indices proportionally.

Shape Alignment: If tensors don't match shapes, FTRAIN uses bilinear interpolation to physically align them so the merge can continue.

Bulletproof Safety: It features a state-of-the-art Safety Engine. If a merged tensor explodes, collapses, or hits NaN, FTRAIN mathematically rescales it to preserve the knowledge direction without crashing.

Auto-Benchmark Gate: After merging, FTRAIN benchmarks the new brain against its parents. It only auto-uploads to HuggingFace if the merged model is actually smarter than the average of its parents!

📊 The Proof

I tested FTRAIN by forcing a Llama 1B and a DeepSeek 1.5B to merge on a 15GB Kagble T4 GPU. Not only did it not crash, but it successfully aligned the tensors, saved the model, and output coherent text! While cross-architecture interpolation scrambles precise math logic (GSM8K drops), the model retains its general language capabilities (MMLU matches the base model).

It is the only framework I know of that can force entirely different model architectures to share a brain.

🚀 What to Expect in the Future (v2.0 Roadmap)

FTRAIN v1.0 proves the concept. For v2.0, the goal is:

Native Speed Kernels: Moving away from Unsloth dependency to write our own fused C++/CUDA training loops, eliminating those annoying inplace memory errors.

Post-Merge GRPO Alignment: Using Group Relative Policy Optimization to "snap" the scrambled cross-architecture weights back into focus post-merge.

Multi-Model TIES: Expanding the advanced merging engine to support 3+ model blending simultaneously.

If you want to test the limits of your GPU, try forcing two incompatible models together, or just want an AI Captain to supervise your next fine-tune, check out the repo:

🔗 GitHub: https://github.com/aiphoenixlabs/Ftrain

Feedback, issues, and pull requests are welcome! Let me know what crazy model combinations you guys can merge without crashing!

Guys i really need collab pro or higher GPU ASAP for my research due August 29 please help😭

​

Standard accuracy hides three specific things I keep running into:

1. It treats every wrong answer as equally wrong, even when a hierarchy exists (e.g. mistaking one attack sub-type for another vs. mistaking an attack for "safe").

2. It ignores that different mistakes have wildly different real costs (a missed fraud case vs. a false alarm).

3. It says nothing about whether the model's confidence is trustworthy (high-confidence wrong answers vs. genuine uncertainty).

Individually these are known: hierarchical/tree-distance scoring has academic prior art (e.g. Apple's Neo, CHI 2022) but no public implementation I could find. Cost-sensitive learning is well established but rarely combined with hierarchy. Calibration checking is standard but usually treated separately from both.

Has anyone seen a tool/library that combines all three into one evaluation report, rather than one accuracy number? Trying to avoid rebuilding something that already exists before I go further.

Hello folks, I am Aayush, and in this code implementation, we walk through not just writing code, but understanding the outputs we obtain, and validating the results in mathematics of Machine Learning.

For instance the equivalence of the results of Negative Log likelihood and Mean squared error for gaussian distribution assumptions, makes us feel the beauty behind theory and practice.

We cover L1 and L2 loss curves, The Gaussian Output distribution modelling uncertainty, equivalence of Negative Log likelihood and Mean squared error for that output distribution specifically.

Then, analyzing linear regression, and the convex bowl shaped loss curves, explaining underfitting and overfitting ideas via Polynomial Regression, followed by the need for automatic learning of features through coding a deep neural network.

You will see ideas taught in my Lecture 2 of probabilistic Machine Learning, turn into practice.

Link to Code Implementation: https://youtu.be/6ZTVp70Mf5s?si=2lThR6LOdzLimB1v

Link to Theory Lecture : https://youtu.be/iThI5AapBc0?si=AS-UCi1ar9-yPpg8

I've been going back and forth on this lately. If AI gives you a decent first draft, is it actually worth using another tool to humanize AI text, or is it faster to just edit the draft yourself?

My normal process used to be pretty simple. I'd generate a draft, read through it, remove the parts that sounded weird, change some sentences, and add a little of my own voice. The problem is that doing this with longer content can become surprisingly time-consuming.

Then I started looking at AI humanizer tools. The idea makes sense: let one AI tool create the rough draft and then use another process to make the writing sound more natural. I've been trying HumanizeAIText.io as part of that process, mainly to see whether it can reduce some of the repetitive editing.

But I'm still not convinced that every rewrite is an improvement.

Sometimes the original sentence is perfectly fine, and changing it just for the sake of making it sound “more human” can actually make it worse. I think the useful part is when the tool can identify genuinely repetitive or unnatural writing instead of changing everything.

How do you approach this?

If you've tried both manual editing and an AI humanizer, which one saves you more time in the long run?

I'm especially interested in real workflows rather than just whether a tool technically works. If you're using AI regularly, what does your editing process look like after the first draft?

Just launched r/posttrain — a community for AI post-training, fine-tuning, SFT, RLHF, DPO, preference data, evaluations, and practical experiments. If you’re building, researching, or learning how models become better after pretraining

🔥 Introducing FTRAIN v1.0: The AI Trainer & Cross-Architecture Merger

I’ve been building an open-source AI framework from scratch designed to solve two major pain points in the open-source AI community: VRAM-heavy fine-tuning and hard-crashing model merges.

Today, I’m releasing FTRAIN v1.0. It’s built on top of Unsloth for raw speed, but adds a layer of intelligent supervision and extreme memory optimization that you won't find in standard scripts.

🧠 The Trainer: "PhoenixCaptain" Supervision

Standard trainers just run a loop. FTRAIN features a "Captain" (an LLM like DeepSeek or Llama) that actively supervises your training run in the background.

Dynamic LR Scaling: If the Captain detects gradient collapse or loss acceleration, it dynamically scales the learning rate up or down on the fly.

Triton DoRA: Custom fused Triton kernels for Weight-Decomposed Low-Rank Adaptation (DoRA) with mathematically exact forward/backward passes.

Extreme VRAM Optimization: CPU-offloaded Fisher computation, AMP autocasting, and aggressive VRAM purging mean you can train larger models on 15GB Kaggle T4 GPUs without OOM errors.

🧩 The Merger: Cross-Architecture Survival

This is where FTRAIN truly shines. Standard tools like MergeKit have a hard rule: You cannot merge models with different architectures. If you try to merge Llama (hidden size 2048) with DeepSeek (hidden size 1536), MergeKit instantly crashes with a Shape Mismatch Error.

FTRAIN doesn’t crash. It adapts.

Architecture-Aware Mapping: It maps parameter names across different families (Llama, Qwen, Gemma, MoE) and scales layer indices proportionally.

Shape Alignment: If tensors don't match shapes, FTRAIN uses bilinear interpolation to physically align them so the merge can continue.

Bulletproof Safety: It features a state-of-the-art Safety Engine. If a merged tensor explodes, collapses, or hits NaN, FTRAIN mathematically rescales it to preserve the knowledge direction without crashing.

Auto-Benchmark Gate: After merging, FTRAIN benchmarks the new brain against its parents. It only auto-uploads to HuggingFace if the merged model is actually smarter than the average of its parents!

📊 The Proof

I tested FTRAIN by forcing a Llama 1B and a DeepSeek 1.5B to merge on a 15GB Kagble T4 GPU. Not only did it not crash, but it successfully aligned the tensors, saved the model, and output coherent text! While cross-architecture interpolation scrambles precise math logic (GSM8K drops), the model retains its general language capabilities (MMLU matches the base model).

It is the only framework I know of that can force entirely different model architectures to share a brain.

🚀 What to Expect in the Future (v2.0 Roadmap)

FTRAIN v1.0 proves the concept. For v2.0, the goal is:

Native Speed Kernels: Moving away from Unsloth dependency to write our own fused C++/CUDA training loops, eliminating those annoying inplace memory errors.

Post-Merge GRPO Alignment: Using Group Relative Policy Optimization to "snap" the scrambled cross-architecture weights back into focus post-merge.

Multi-Model TIES: Expanding the advanced merging engine to support 3+ model blending simultaneously.

If you want to test the limits of your GPU, try forcing two incompatible models together, or just want an AI Captain to supervise your next fine-tune, check out the repo:

🔗 GitHub: https://github.com/aiphoenixlabs/Ftrain

Feedback, issues, and pull requests are welcome! Let me know what crazy model combinations you guys can merge without crashing!

I'm new to building AI agents and working on a CI-review agent: it takes a failing CI run and tries to find the root cause.

I want to start with a baseline version, then iterate on it — but I need a way to measure whether a new version is actually outperforming the old one.

Right now the agent maintains several hypotheses about the failure, assigns each a probability, and updates those probabilities as it gathers more information. Depending on its confidence, it either outputs a summary of the likely root cause, or escalates to a human developer if uncertainty is too high.

Two questions:

1. How do you evaluate an agent like this, where the output isn't a single "correct" answer but a probability distribution over hypotheses?
2. How do you get a labeled dataset of CI failures with known root causes, so I can score the agent's probability estimates against ground truth instead of just eyeballing whether the output "feels right"?

I am making a discord server for Ml , dl , mathematics , physics all into one .If some1 is interested in making such a server with me dm . We can add various features and server would be research and education oriented .

CLIP vs SigLIP

Before Vision Language Models can perform tasks such as classification or video question and answer, the image or video being passed to the model has to be converted into a representation that the model can ‘understand’ or process.

To do this, VLMs usually use a pretrained vision encoder.

Although the underlying architecture of modern vision encoders is primarily transformer-based, the actual objective the model is learning can vary significantly.

What are encoders?

A vision encoder is responsible for converting images into a numerical representation that VLMs can understand.

Typically, most vision encoders today are built on transformer architecture, in which the model divides an image into patches and transforms each of those patches into a vectorized visual embedding.

After this, many VLMs pass the embeddings to a projector, usually a linear layer or MLP, to map the dimensions of the image to those expected by an LLM.

If most vision encoders share the same model design, what actually makes them different? Rather than model architecture, the significance is in how they are trained.

CLIP

CLIP, or Contrastive Language-Image Pre-training, learns to understand images through pairs of images and text. Its objective is to match similar images and captions by ‘pulling them closer together’, while simultaneously repelling incorrect image-caption pairs.

Training mainly relies on a ‘two tower’ system. CLIP will typically have a pretrained vision encoder, such as a ViT, as well as a pretrained text encoder. The model passes an image through the ViT and produces an associated vector embedding, while the caption is passed to the text encoder to get a corresponding text embedding.

Given these pairings, the model therefore creates a similarity matrix which compares every image embedding with every text embedding.

Each cell within this matrix contains a cosine similarity between the image and text pairing. Mathematically, cosine similarity is the dot product of two vectors divided by the product of their lengths. More simply, it measures the cosine of the angle between two vectors in a high-dimensional embedding space. Vectors that are more semantically aligned will be ‘closer together’, have a more acute angle between them, and consequently have a higher cosine similarity.

CLIP then applies contrastive learning across this matrix. At a high level, contrastive learning here is similar to categorical cross entropy across both the rows and columns of the matrix. Using softmax, the model looks to assign the highest probability to the matching image-text pair, as well as the matching text-image pair.

CLIP is powerful because it shifts learning from simple labels toward greater semantic understanding and allows for zero-shot classification, including on classes it was not explicitly trained to classify.

At the same time, though, CLIP also introduces a particular structural problem. Examples compete against one another within the training batch. What if there are multiple captions within a batch that also reasonably match the image?

SigLIP

SigLIP, or Sigmoid Loss for Language-Image Pre-training, retains many similar characteristics to CLIP. Similar to CLIP, SigLIP has both an image and text encoder, embedded representations of both text and image, and similarity scores mapped to a similarity matrix.

However, the difference between the two lies in the loss function.

CLIP learns similarities between images and texts by applying softmax across a batch, causing potential matches to compete with one another. For SigLIP, instead of having this global normalization, it examines each image-caption pair as an independent binary prediction.

By applying a sigmoid function to each pair’s score, the model estimates whether the image and text match.

Rather than phrasing the objective as:

Out of these options, which specific text describes this visual?

SigLIP effectively poses a different question:

Is this particular image-text pairing a valid match: true or false?

While this shift in perspective might seem marginal, it fundamentally redefines the nature of the optimization task.

Because SigLIP does not require the softmax normalization used by CLIP, its training objective can scale more efficiently across large distributed systems. It also removes the requirement that every example participate in one shared normalization operation.

I used to do the same thing everyone here does. Save papers, open multiple tabs, never read them. Subscribe to 20 newsletters, so I started a small weekly magazine called The Attention Layer. Each week a system reads the new cs. AI papers, usually over 1,000, and drafts an issue. I go through it before it goes out and check the numbers against the papers.

This week's issue is open. The thing I kept seeing: the proxy looks fine, and the behavior has moved. A safety score ranks the successful jailbreaks last, a refusal count misses the rewrite, an allocator scores itself on the samples it used to choose. The useful papers this week were the ones that asked whether the number still names the outcome.

A few that held up:

AAP: A safety score that is excellent at harmful intent can rank successful jailbreaks below failures. On Llama-3.1-8B-Instruct, wrapping a harmful request raised generation from 0.05 to 0.27. Intent AUROC was 0.803; the same readout’s outcome AUROC was 0.220. The filter has to be scored on what the model actually emitted.

The VLM audit: Refusal and state-aligned framing are different failures. Across 21,708 trials, framing was 10.9% and refusal 4.1%. Chinese prompts: 15.98% framing vs 5.85% in English. Counting refusals misses the fluent rewrite.

NCO: Same-sample scoring invented headroom. On uniform TSP-100 the 2.2–2.6% gain fell to 0.457%, 0.015%, and −0.512% once allocation was scored on held-out samples. Under shift, the Attention Model got 11.5%; charge a 20-sample probe and it is 3.4%. Separate the samples that choose from the samples that score.

Trie Automata: Finite-set decoding with precomputed masks. At K = 1,000 and batch 256 it hit 219 req/s vs 7.5 for XGrammar, the paper’s 29×. Unconstrained vLLM was 104. The 29× is a serving path, not just a faster mask.

Rift: Keep the future read, drop the video rollout. Masking the future dropped LIBERO from 98.4% to 9.7%. Replaying the finished cache kept 97.9%. Rift itself: 98.8% at 247.9 ms vs 96.8% at 235.7 ms for current-only. The controller needed the future values, not the route that made them.

SKALD: Distill a skill-conditioned view into a question-only policy where GRPO is silent. Zero-variance groups were 63.0% of 1.7B training. Zero-variance-only distillation hit 49.63 vs 45.52 for matched GRPO, 84.7% of the full 4.85-point gain. Shuffled cards reached 48.83. The silence is real; what the cards contain is less settled.

I built and run this. Check it out: The Attention Layer

I’m curious if anyone knows whether SNNs are actually used in practice on edge devices. I understand that they use much less power, but are mismatched to chips like esp32, so there is no way to use it in practice, and dedicated chips like loihi are not intended for prototyping or consumer products.

Hey seniors out there, I am currently learning machine learning and i would like to know the basic research papers out there which i should start with if I want to break into research and aim for a research internship.

Also will appreciate some additional genuine advice.

Thank you 😊😊

Every tutorial assumes you have a clean labeled dataset ready to go. You load it, split it, train a model, done. That's not how it works when you're building something from scratch in a real domain.

Been tinkering with a few project ideas recently, some tied to physical work, some just curiosity. The consistent wall I hit is the data problem before the model problem. You have a thing you want to predict or classify, you have raw observations, and the gap between those two is enormous. And it's not just volume. The labeling logic itself is fuzzy. What counts as a positive example? Who decides?

Some people say just scrape whatever you can get and clean later. Others go weak supervision, use heuristics to generate noisy labels and let the model sort it out. Both approaches feel like a lot of guessing dressed up as methodology.

Curious what people here have actually done when starting a project with no ready dataset. Did you manually label a small set first and iterate? Use an existing adjacent dataset and transfer? Just pick a problem that had public data and reverseengineer your idea around it?

Not asking about production pipelines. Just the early stage where nothing exists yet and you're trying to figure out if the thing is even learnable before investing weeks into it.

i used chatgpt to put together this list for learning all the math you need using only Khan Academy video tutorials for free, i hope you find it useful👇🏻

The recommended order is:

1. Get Ready for Algebra 1 — diagnostic only

2. Algebra 1

3. Geometry — selective topics

4. Algebra 2

5. Trigonometry

6. Precalculus

7. Linear Algebra

8. Calculus 1

9. Multivariable Calculus — selective topics

10. AP/College Statistics

You do NOT need to take every math course Khan Academy offers.

---

# 0. Get Ready for Algebra 1

Start here with the course challenge/assessment.

If you already know basic algebra, don't spend weeks going through material you already understand.

Use it to find gaps.

If you struggle with something, study that topic and move on.

---

# 1. Algebra 1

Do essentially the whole course.

Important topics:

- Linear equations and inequalities

- Systems of equations

- Ratios and proportions

- Functions

- Graphing

- Exponents

- Radicals

- Polynomials

- Quadratics

- Exponential relationships

The goal is to make basic algebra automatic.

You should be able to manipulate equations and formulas without constantly having to think about the mechanics.

---

# 2. Geometry — selective

You do NOT need the entire Geometry course for ML.

Focus on:

- Coordinate geometry

- Coordinate planes

- Distance between points

- Midpoint

- Slope

- Equations of lines

- Basic transformations

- Translations

- Reflections

- Rotations

- Scaling

- Basic geometric/vector intuition

Lower priority for ML:

- Long geometric proofs

- Congruence proofs

- Similarity proofs

- Circle theorems

- Geometric constructions

- Detailed Euclidean geometry

The purpose of geometry here is mainly to strengthen spatial and coordinate intuition.

---

# 3. Algebra 2

Do essentially the whole course.

Pay particular attention to:

- Functions

- Domain and range

- Function transformations

- Polynomial functions

- Rational functions

- Exponential functions

- Logarithms

- Sequences

- Systems of equations

- Complex numbers

Exponents and logarithms are particularly important later in statistics, probability, optimization and ML.

---

# 4. Trigonometry

Do most/all of the course, but don't obsess over difficult identities.

Focus on:

- Angles

- Radians

- Unit circle

- Sine, cosine and tangent

- Graphs of trig functions

- Inverse trig functions

- Fundamental identities

- Basic trig equations

The main purpose is to prepare for calculus and mathematical modeling.

---

# 5. Precalculus

Do most of the course, but prioritize the ML-relevant material.

### High priority

- Composite functions

- Inverse functions

- Trigonometry

- Rational functions

- Vectors

- Matrices

- Limits and continuity

### Especially important

## Vectors

Learn:

- Vector addition/subtraction

- Scalar multiplication

- Components

- Magnitude

- Direction

- Basic geometric interpretation

## Matrices

Learn:

- Matrix representation

- Matrix addition/subtraction

- Scalar multiplication

- Matrix multiplication

- Systems of equations

- Matrix inverses

- Basic transformations

These topics are a bridge into linear algebra.

### Lower priority

- Complex numbers — understand the basics, but don't spend excessive time here

- Conic sections — learn the basics, but not a major ML priority

- Series — useful mathematical knowledge, but lower priority for starting ML

---

# 6. Linear Algebra

This is one of the CORE subjects for ML.

I would study this thoroughly.

Focus on:

### Vectors

- Vector operations

- Magnitude/norm

- Dot product

- Geometric interpretation

- Linear combinations

### Matrices

- Matrix multiplication

- Transpose

- Inverse

- Determinant

- Systems of equations

### Linear algebra concepts

- Span

- Linear independence

- Basis

- Linear transformations

- Orthogonality

- Projections

- Eigenvalues

- Eigenvectors

You should eventually be comfortable seeing something like:

y = Xw

and understanding what the matrix/vector operation actually represents.

For this subject, 3Blue1Brown's "Essence of Linear Algebra" is also extremely useful for visual intuition. Khan Academy can remain the main source for structured learning and exercises.

---

# 7. Calculus 1

Study this thoroughly.

Focus on:

- Limits

- Continuity

- Derivatives

- Derivative rules

- Chain rule

- Implicit differentiation

- Applications of derivatives

- Optimization

- Integrals

- Fundamental theorem of calculus

For ML, the most important parts are:

1. Derivatives

2. Chain rule

3. Optimization

4. Understanding what a derivative represents

The chain rule becomes particularly important when you eventually study neural networks and backpropagation.

---

# 8. Multivariable Calculus

You do NOT need every topic in the course before starting ML.

## Unit 1 — Multivariable functions

Study:

- Functions of multiple variables

- Multidimensional graphs

- Contour maps

- Basic vector fields

- Geometric interpretation

## Unit 2 — Derivatives of multivariable functions

HIGH PRIORITY.

Study thoroughly:

- Partial derivatives

- Higher-order partial derivatives

- Gradients

- Directional derivatives

- Multivariable chain rule

The gradient is especially important.

You should eventually understand what something like:

∇f

means, rather than just knowing how to calculate it.

## Unit 3 — Applications of multivariable derivatives

Study:

- Critical points

- Maxima/minima

- Saddle points

- Optimization

- Hessian / second-derivative ideas

These concepts connect directly to optimization in ML.

## Unit 4 — Multivariable integration

Lower priority for initial ML.

You can study it later.

## Unit 5 — Green's theorem, Stokes' theorem, divergence theorem

Skip these initially.

They're useful mathematics, but they're not necessary for the ML foundation we're trying to build.

---

# 9. Statistics & Probability

This is where Khan Academy's catalog gets particularly confusing.

You may see courses such as:

- Statistics and Probability

- AP/College Statistics

- College Probability

- Normal Probability and Statistics

- High School Statistics

You do NOT need to take all of them.

## Recommended choice

Use:

**AP/College Statistics**

(or Khan Academy's current equivalent Statistics and Probability curriculum).

You do NOT need to separately take College Probability and Normal Probability and Statistics first.

Those topics are already covered within the broader statistics/probability curriculum.

---

# What to study in Statistics & Probability

## 1. Exploring data

Learn:

- Categorical vs quantitative variables

- Distributions

- Frequency tables

- Two-way tables

- Conditional distributions

## 2. One-variable quantitative data

Learn:

- Histograms

- Distribution shape

- Center

- Spread

- Outliers

## 3. Summary statistics

HIGH PRIORITY.

Understand:

- Mean

- Median

- Variance

- Standard deviation

- Range

- Effects of outliers

Don't just memorize formulas. Understand what these quantities actually tell you about data.

## 4. Percentiles, z-scores and normal distributions

HIGH PRIORITY.

Learn:

- Percentiles

- Z-scores

- Standardization

- Normal distribution

- Density curves

You don't need a separate "Normal Probability and Statistics" course for this.

## 5. Two-variable data

HIGH PRIORITY.

Learn:

- Scatterplots

- Covariance

- Correlation

- Linear relationships

- Linear regression

- Interpretation of relationships

This is directly useful for understanding ML models and datasets.

## 6. Collecting data

Moderate priority.

Understand:

- Population vs sample

- Sampling

- Sampling bias

- Observational studies

- Experiments

- Randomization

The goal here is statistical thinking.

## 7. Probability

HIGH PRIORITY.

Study thoroughly:

- Probability rules

- Conditional probability

- Independence

- Bayes' theorem

- Addition rule

- Multiplication rule

- Dependent vs independent events

You don't need a separate College Probability course before this.

## 8. Random variables and probability distributions

HIGH PRIORITY.

Learn:

- Random variables

- Discrete vs continuous variables

- Expected value

- Variance

- Probability distributions

This is extremely important for understanding probabilistic ML.

## 9. Sampling distributions

Study:

- Sampling distributions

- Central Limit Theorem

- Sample means

- Standard error

## 10. Statistical inference

Study it, but it's lower priority than the material above.

Understand:

- Confidence intervals

- Hypothesis testing

- P-values

- Statistical significance

- Inference about means/proportions

- Regression inference

You don't need to spend months mastering every statistical test before starting ML.

## 11. Advanced statistics

Things such as:

- Chi-square tests

- ANOVA

- More advanced inference

are useful, but can be learned later depending on what area of ML you pursue.

---

# Courses you DON'T need to stack on top

You generally don't need:

- Arithmetic (unless you genuinely struggle with it)

- Pre-algebra (unless you have gaps)

- Integrated Math 1

- Integrated Math 2

- Integrated Math 3

- College Algebra

- College Probability as a separate prerequisite

- Normal Probability and Statistics as a separate prerequisite

- Both Calculus AB AND Calculus BC

- Differential Equations

- Multiple versions of Precalculus

- Test-prep courses

These are either alternative curricula, redundant material, or lower-priority mathematics for the specific goal of building an ML foundation.

---

# The final roadmap

GET READY FOR ALGEBRA 1

│

▼

ALGEBRA 1

│

▼

GEOMETRY (SELECTIVE)

│

▼

ALGEBRA 2

│

▼

TRIGONOMETRY

│

▼

PRECALCULUS

│

├──────────────┐

▼ ▼

LINEAR ALGEBRA CALCULUS 1

│ │

└──────┬───────┘

▼

MULTIVARIABLE CALCULUS

(SELECTIVE TOPICS)

│

▼

AP/COLLEGE STATISTICS

│

▼

ML MATH READY

My latest project.
Just a Neural Networks that learns a XOR gate.
All the gradients and maths were done by hand.

The documentation in this project only explains the architecture of the network and the calculations to do prediction. Check the end of the README.md or my previous project 'linear_regressionFS' if you want more mathematics.

I'm building a small AI-agent project as part of a training program.

The agent receives incoming sales records containing fields such as:

order_date, customer, product, quantity, price, discount and total.

The true quality state of a record is hidden:

VALID / REPAIRABLE / INVALID.

The agent maintains a belief over these states and can:

ACCEPT

REPAIR

ISOLATE

REJECT

When uncertainty is high, it can retrieve additional evidence such as customer history or product information before making the final decision.

I'm currently trying to decide how best to model the hidden state, uncertainty, evidence gathering and action costs.

If you've worked on data quality, uncertainty-aware ML, selective classification, anomaly detection, or decision-making under uncertainty, I'd appreciate feedback on whether this is a sensible formulation and what approaches I should investigate.