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Peyman Milanfar Profile picture
@docmilanfar
Oct 8, 2022 • 6 tweets • 4 min read • Read on X
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Yesterday @ #MadeByGoogle we also announced the latest on the Super Res Zoom feature on #Pixel7Pro

It's a project my team's been involved in since '18. This year, our teams've made it so much more powerful. You can zoom up to 30x. Let me show you in a 🧵

That👆one was the ultra-wide lens (0.5x).

This 👇one starts at 1x and get closer....
And closer....
That's not close enough - let's get closer ...
we're almost there....
And finally we're at 30x hybrid optical/digital zoom, seeing the top of One World Trade Center miles away.

I hope this gives you an idea what the zoom experience looks like on #Pixel7Pro. You can see the whole sequence in an album:
photos.app.goo.gl/SoV1s7EU6c7APb…
PC: Alex Schiffhauer

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More from @docmilanfar

Peyman Milanfar Profile picture
Feb 16
Images aren’t arbitrary collections of pixels -they have complicated structure, even small ones. That’s why it’s hard to generate images well. Let me give you an idea:

3×3 gray images represented as points in ℝ⁹ lie approximately on a 2-D manifold: the Klein bottle!

1/4 Image
Images can be thought of as vectors in high-dim. It’s been long hypothesized that images live on low-dim manifolds (hence manifold learning). It’s a reasonable assumption: images of the world are not arbitrary. The low-dim structure arises due to physical constraints & laws

2/4 Image
But this doesn’t mean the “low-dimensional” manifold has a simple or intuitive structure -even for tiny images. This classic paper by Gunnar Carlsson gives a lovely overview of the structure of data generally (and images in particular). Worthwhile reading.

3/4 Image
Read 4 tweets
Peyman Milanfar Profile picture
Feb 8
Michael Jordan gave a short, excellent, and provocative talk recently in Paris - here's a few key ideas

- It's all just machine learning (ML) - the AI moniker is hype

- The late Dave Rumelhart should've received a Nobel prize for his early ideas on making backprop work

1/n Image
The "Silicon Valley Fever Dream" is that data will create knowledge, which will lead to super intelligence, and a bunch of people will get very rich.....

2/n Image
.... yet the true value of technologies like LLMs is that we're getting the benefit of interacting with the collective knowledge of many many individuals - it's not that we will produce one single uber-intelligent being

3/n Image
Read 5 tweets
Peyman Milanfar Profile picture
Jan 26
How are Kernel Smoothing in statistics, Data-Adaptive Filters in image processing, and Attention in Machine Learning related?

I wrote a thread about this late last year. I'll repeat it here and include a link to the slides at the end of the thread.

1/n Image
In the beginning there was Kernel Regression - a powerful and flexible way to fit an implicit function point-wise to samples. The classic KR is based on interpolation kernels that are a function of the position (x) of the samples and not on the values (y) of the samples.

2/n Image
Instead of a fixed smoothing parameter h, we can adjusted it dynamically based on the local density of samples near the point of interest. This enables accounting for variations in the spatial distribution of samples, but doesn't take into account of the values of samples

3/n Image
Read 11 tweets
Peyman Milanfar Profile picture
Dec 20, 2024
Years ago when my wife and I we were planning to buy a home, my dad stunned me with a quick mental calculation of loan payments.

I asked him how - he said he'd learned the strange formula for compound interest from his father, who was a merchant in 19th century Iran.

1/4 Image
The origins of the formula my dad knew is a mystery, but I know it has been used in the bazaar's of Iran (and elsewhere) for as long as anyone can remember

It has an advantage: it's very easy to compute on an abacus. The exact compounding formula is much more complicated

2/4 Image
I figured out how the two formulae relate: the historical formula is the Taylor series of the exact formula around r=0.

But the crazy thing is that the old Persian formula goes back 100s (maybe 1000s) of years before Taylor's, having been passed down for generations

3/4 Image
Read 4 tweets
Peyman Milanfar Profile picture
Dec 8, 2024
How are Kernel Smoothing in statistics, Data-Adaptive Filters in image processing, and Attention in Machine Learning related?

My goal is not to argue who should get credit for what, but to show a progression of closely related ideas over time and across neighboring fields.

1/n Image
In the beginning there was Kernel Regression - a powerful and flexible way to fit an implicit function point-wise to samples. The classic KR is based on interpolation kernels that are a function of the position (x) of the samples and not on the values (y) of the samples.

2/n Image
Instead of a fixed smoothing parameter h, we can adjusted it dynamically based on the local density of samples near the point of interest. This enables accounting for variations in the spatial distribution of samples, but doesn't take into account of the values of samples

3/n Image
Read 11 tweets
Peyman Milanfar Profile picture
Dec 3, 2024
“On a log-log plot, my grandmother fits on a straight line.”
-Physicist Fritz Houtermans

There's a lot of truth to this. log-log plots are often abused and can be very misleading

1/5 Image
A plot of empirical data can reveal hidden phenomena or scaling. An important and common model is to look for power laws like

p(x) ≃ L(x) xᵃ

where L(x) is slowly varying, so that xᵃ is dominant

Power laws appear all over physics, biology, math, econ. etc., however...

2/5
...just because on a log-log plot your data looks like a line, you can't conclude that you're looking at a power law

In fact, a roughly straight behavior on a log-log scale is like a necessary condition, but it is not sufficient for power-law behavior. Take this example:

3/5 Image
Read 5 tweets

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