Light computes any desired linear transform without a digital processor

https://phys.org/news/2021-09-desired-linear-digital-processor.html

81 34 5 years ago

Gravyness• 5 years ago

Would it be possible to develop a computer from linear transformations? Suppose registers, op codes and their parameters were represented as images, and at each clock a led grid is turned on with the current computer state, the light propagating into a sequence of diffractive surfaces to generate the next state through linear transformations, which is picked up and its result is used to change the led grid in the right places. Even if such a thing could be turing complete I guess the current computing problem is memory retrieval time and not internal cpu processing time...

wiml• 5 years ago

You really need some nonlinear functions if you want to compute interesting things (and you can't build nonlinear functions out of purely linear parts).

tines• 5 years ago

Is nand nonlinear?

vlovich1232• 5 years ago

Can you expand on that point a bit?

Deep learning approximates non-linear functions and the binary functions at the heart of CPUs are inherently linear no? That would seem to contradict the argument that you can’t build non linear functions out of linear parts. As a general concept, it seems generally possible to approximate non linear functions with linear ones, which I imagine is how deep learning works. I’m not a domain expert at any of these math topics though so happy to learn more.

https://mathinsight.org/approximating_nonlinear_function_by_... https://en.m.wikipedia.org/wiki/Linearization https://stackoverflow.com/questions/4908893/what-logic-gates...

ajb3• 5 years ago

Actually, you can do logic in linear (matrix) operations. This is what quantum computers do. Eg, if you look at the toffoli gate: https://en.wikipedia.org/wiki/Toffoli_gate it's a universal logic function (any logic function can be constructed using it) but in its form as a permutation matrix, it's a linear matrix operation.

The catch is that its input is in the form of a vector having 1 entry for each possible value of the input in actual bits, which is an exponential increase in space. But, it is an existence proof that in some sense, you can do logic with linear functions, as long as you don't mind some kind of weird representation of your inputs and outputs.

What I don't know is, whether you can use linear operations for logic with a smaller than exponential space increase.

Buttons8403• 5 years ago

Would it be possible to develop a computer from linear transformations?

No, a program consisting of a billion linear transformations could be simplified to a single linear transformation. The halting problem would be solved, all programs can halt. All calculations, no matter how many linear transformations they consist of, could be simplified to a single linear transformation. This would be absurdly good, but still absurd, thus impossible.

Buttons8403• 5 years ago

A key insight is that any combinations of linear transformations is a linear transformation. Got a sequence of a billion linear transformation? The entire sequence can be expressed as a single linear transformation. Thus, no matter how many linear transformation you perform, you're never able to exceed the abilities of a single linear transformation.

ac42• 5 years ago

Would it be possible to develop a computer from linear transformations?

Yes. The transition function of Turing machines and the working tape can be represented as linear transformations. For quantum computers, these transformations even need to be unitary.

This very standard construction does not conflict with the halting problem: you don't know how often you have to apply this linear transform to your state vector until you got your result.

Loranubi• 5 years ago

Similar co-processors have been used for some time https://en.wikipedia.org/wiki/Optical_computing#Optical_Four...

xyzzy21• 5 years ago

This is NOT new.

This type of processing was being used in guidance systems of missiles in the 1980s.

gus_massa• 5 years ago

The problem is the title, but remember that the researchers don't write the title of the press article.

It's well known that you can compute any desired linar transformation with light and lens, diffraction gratings and similar stuff. I've see people calculating the wavelets transform with a similar equipment, like 10 years ago.

The interesting part of the research article is that they got a better method to design the lens, diffraction gratings and similar stuff to calculate the transformation. This is somewhat explained in the article, but totally lost in the title.

samaman• 5 years ago

Just reminds me of Chaco Canyon and how eloquently light transforms can be used for many purposes https://www2.hao.ucar.edu/Education/SolarAstronomy/sun-dagge....

amelius• 5 years ago

Title should say: any desired fixed linear transform.

(Which greatly reduces the number of applications of the technique)

Gravityloss• 5 years ago

Maybe you could have liquid crystals or other equivalent optical routing mechanisms. The pipeline can process billions of computations per second, but changing the pipeline takes milliseconds. Talk about SIMD...

imtringued• 5 years ago

You mean a field programmable optics array.

twistedpair• 5 years ago

This is old school tech.

For example, I was tought how this worked in satillite image analysis optical computers (e.g. Cold War tech) when getting my optics degree.

Jeff_Brown• 5 years ago

For machine learning, an important nonlinear activation curve, the ReLU curve, seems like it might be achievable optically. Just bend the beam, and if it bends far enough, run it into something black.

BenoitP• 5 years ago

A similar approach has been tried by using the micro mirrors arrays from projectors:

https://lighton.ai/publications/

They use the mirrors to do random projections very rapidly, and collecting the results on a CMOS receptor. Somehow the projection help tackle high-dimensional data.

Intro to how the math would be done at the beginning, meat of the device details at 20:10 : https://youtu.be/0QtY4_UJF0w

Funny how you can do a mathematical projection using a projector!

Light computes any desired linear transform without a digital processor

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