Google DeepMind's open-sourced AlphaGeometry blends "fast thinking" (like intuition) with "slow thinking" (like careful, conscious reasoning) to enable a big leap forward in A.I. capability and match human Math Olympiad gold medalists on geometry problems.
KEY CONTEXT
• A couple weeks ago, DeepMind published on AlphaGeometry in the prestigious journal peer-reviewed Nature.
• DeepMind focused on geometry due to its demand for high-level reasoning and logical deduction, posing a unique challenge that traditional ML models struggle with.
MASSIVE RESULTS
• AlphaGeometry tackled 30 International Mathematical Olympiad problems, solving 25. This outperforms human Olympiad bronze and silver medalists' averages (who solved 19.3 and 22.9, respectively) and closely rivals gold medalists (who solved 25.9).
• This new system crushes the previous state-of-the-art A.I., which solved only 10 out of 30 problems.
• Beyond solving problems, AlphaGeometry also generates understandable proofs, making A.I.-generated solutions more accessible to humans.
HOW?
• AlphaGeometry uses a new method of generating synthetic theorems and proofs, simulating 100 million unique examples to overcome the limitations of (expensive, laborious) human-generated proofs.
• It combines a neural (deep learning) language model for intuitive guesswork with a symbolic deduction engine for logical problem-solving, mirroring "fast" and "slow thinking" processes akin to human cognition (per Daniel Kahneman's "Thinking, Fast and Slow" book).
IMPACT
• A.I. that can "think fast and slow" like AlphaGeometry could generalize across mathematical fields and potentially other scientific disciplines, pushing the boundaries of human knowledge and problem-solving capabilities.
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Daily Habit #8: Math or Computer Science Exercise
This article was originally adapted from a podcast, which you can check out here.
At the beginning of the new year, in Episode #538, I introduced the practice of habit tracking and provided you with a template habit-tracking spreadsheet. Then, we had a series of Five-Minute Fridays that revolved around daily habits I espouse, and that theme continues today. The habits we covered in January and February were related to my morning routine.
Starting last week, we began coverage of habits on intellectual stimulation and productivity. Specifically, last week’s habit was “reading two pages”. This week, we’re moving onward with doing a daily technical exercise; in my case, this is either a mathematics, computer science, or programming exercise.
The reason why I have this daily-technical-exercise habit is that data science is both a limitlessly broad field as well as an ever-evolving field. If we keep learning on a regular basis, we can expand our capabilities and open doors to new professional opportunities. This is one of the driving ideas behind the #66daysofdata hashtag, which — if you haven’t heard of it before — is detailed in episode #555 with Ken Jee, who originated the now-ubiquitous hashtag.
Read MoreMy Favorite Calculus Resources
It's my birthday today! In celebration, I'm delighted to be releasing the final video of my "Calculus for Machine Learning" YouTube course. The first video came out in May and now, ten months later, we're done! 🎂
We published a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday since May 6th, 2021. So happy that it's now complete for you to enjoy. Playlist is here.
More detail about my broader "ML Foundations" curriculum (which also covers subject areas like Linear Algebra, Probability, Statistics, Computer Science) and all of the associated open-source code is available in GitHub here.
Starting next Wednesday, we'll begin releasing videos for a new YouTube course of mine: "Probability for Machine Learning". Hope you're excited to get going on it :)
Jon’s Machine Learning Courses
his article was originally adapted from a podcast, which you can check out here.
For last week’s Five-Minute Friday episode, I provided a summary of the various methods of undertaking my deep learning curriculum, be it via YouTube, my book, or the associated repository of GitHub code. I mentioned at the end of the episode that while teaching this deep learning content to students online and in-person, I discovered that many folks could use a primer on the foundational subjects that underlie machine learning in general and deep learning in particular. So after publishing all my deep learning content, I set to work on creating content that covers these subjects that are critical to understanding machine learning expertly — namely, those subjects are linear algebra, calculus, probability, statistics, and computer science.
Way back in Episode #474 of this podcast, I detailed why these particular subject areas form the sturdy foundations of what I call the Machine Learning House . As a quick recap, the idea is that to be an outstanding data scientist or ML engineer, it doesn't suffice to only know how to use machine learning algorithms via the abstract interfaces that the most popular libraries (e.g., scikit-learn, Keras) provide. To train innovative models or deploy them to run performantly in production, an in-depth appreciation of machine learning theory may be helpful — or even essential. To cultivate such an in-depth appreciation of ML, one must possess a working understanding of the foundational subjects, which again are linear algebra, calculus, probability, stats, and computer science:
Read MoreFinding the Area Under the ROC Curve
In this week's tutorial, we use Python code to find the area under the curve of the receiver operating characteristic (the "ROC curve"). This is a machine learning-specific application of integral calculus.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
This is the penultimate video in my Calculus course! After ten months of publishing it, the final video will be released next week :)
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
Definite Integral Exercise
My recent videos have covered how to find Definite Integrals manually as well as how to find them computationally using Python code. This week's video is an exercise that tests comprehension of both approaches.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
Numeric Integration with Python
Having detailed how to integrate equations by hand over the past few weeks, this week's video tutorial uses Python code to introduce how to find Definite Integrals computationally — and therefore automatically.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
Definite Integrals
In recent weeks, my videos introduced Indefinite Integration. Today, we go a step further to calculate *Definite* Integrals. This allows us to find the area under a curve, which is essential for many machine learning models.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
Indefinite Integral Exercises
If you watched last week's video on the integral calculus rules (or if you already feel confident about them!), you can use this week's video to test your comprehension of the topic.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
The Integral Calculus Rules — Topic 86 of Machine Learning Foundations
Integral Calculus Rocks! I mean, Integral Calculus Rules! I mean, this video covers the Integral Calculus Rules 😉... namely, the Power Rule, the Constant-Multiple Rule, and the Sum Rule.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
What Integral Calculus Is
What is Integral Calculus and why is it essential to Machine Learning? This week's video answers those questions while also explaining how integral calculus works at a high level and detailing its characteristic notation.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
The Receiver-Operating Characteristic (ROC) Curve
In this video, we work through a simple example — with real numbers — to demonstrate how to calculate the ROC Curve, an enormously useful metric for quantifying the performance of a binary classification model.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
Binary Classification
Last week, I kicked off a series of YouTube videos on Integral Calculus. To provide a real-world Machine Learning application to apply integral calculus to, today's video introduces what Binary Classification problems are.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
Integral Calculus - The Final Segment of Calculus Videos in my ML Foundations Series
After several months of publishing videos on the Differential branch of Calculus, with today's video we turn our focus toward the *Integral* branch. As ever, applications of this math to Machine Learning remain central.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
Exercise on Higher-Order Partial Derivatives
To cap off an epic four-month sequence of videos on Partial-Derivative Calculus, today's YouTube video features an exercise on Higher-Order Partial Derivatives. Next week, a new topic area begins: Integral Calculus!
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
Higher-Order Partial Derivatives
This week's YouTube video introduces higher-order derivatives for multi-variable functions, with a particular focus on the second-order partial derivatives that abound in machine learning.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
Backpropagation
This week's video explains the relationship between Partial-Derivative Calculus and the Backpropagation ("Backprop") approach used widely in training Artificial Neural Networks, including Deep Learning networks.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
The Gradient of Mean Squared Error
For this week's YouTube video, we manually derive the gradient of Mean Squared Error (popular in ML to quantify accuracy). We then use the Python library PyTorch to obtain the same result and to visualize ML in action.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
Gradient Descent (Hands-on with PyTorch)
In my preceding YouTube videos, we detailed exactly what the gradient of cost is. With that understanding, today we dig into what it means to *descend* this gradient and fit a machine learning model.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.
The Gradient of Quadratic Cost
In this week's video, we derive the Partial Derivatives of Quadratic Cost with respect to the parameters of a simple regression model. This derivation is essential to understanding how machines learn via Gradient Descent.
We publish a new video from my "Calculus for Machine Learning" course to YouTube every Wednesday. Playlist is here.
More detail about my broader "ML Foundations" curriculum and all of the associated open-source code is available in GitHub here.