17 ms·

Can you compute a neural network this way? Or do other forms of useful computation?

by api 4y ago

Enginerrrd 4y ago
If I understand correctly that's sort of exactly what this is. The geometry of the diffraction gratings encodes a forward propagation model trained as classifier of the number "2". I don't quite understand the mathematics of how it was trained, but they were able to discretize the geometry of those layers somehow into little 0.4mm pixels of "trainable diffractive neurons" and they simulated light transmission through the layers to compute a loss function. I'm really surprised that this was computationally feasible. Simulation of light through the gratings must have been cheap enough as a function evaluation to train the network.
- Lramseyer 4y ago
  I would imagine that you generate the desired transform function of a diffractive structure rather than the structure itself, because the structure is ultimately derived from the transform function. Since the transform function is basically a 2D fourier transform and a spatial frequency/phase plot, it's not _that_ computationally costly. Once you settle on functions you like, you then generate and or simulate a diffractive structure and see if it behaves how you expect.
Lramseyer 4y ago
Sort of, I didn't dive too far into the math, but it looks like each diffractive structure is akin a layer of a neural net, which is tuned for a set of spatial frequencies and phases, which when combined (like layers of a neural net) to form recognition of more complex objects. There are a few gotchas in that statement though - for one, I didn't dive too far into the math, and I would assume that the convolutional algorithms as well as the underlying matrix functions may be different. But at the end of the day, you're approximating a complex function using an array of simple functions with different weights and scale factors. The other gotcha is that diffractive structures use monochromatic light, so it's probably not too useful in most normal situations with normal light sources.
SiempreViernes 4y ago
It can do the same sort of computation work any stack of analogue filters can do: it does one thing very fast and if you want something else done you must create those filters first and the frame holding the stack is of no help at all.

Can you compute a neural network this way? Or do other forms of useful computation?

by api 4y ago

Can you compute a neural network this way? Or do other forms of useful computation?

If I understand correctly that's sort of exactly what this is. The geometry of the diffraction gratings encodes a forward propagation model trained as classifier of the number "2". I don't quite understand the mathematics of how it was trained, but they were able to discretize the geometry of those layers somehow into little 0.4mm pixels of "trainable diffractive neurons" and they simulated light transmission through the layers to compute a loss function. I'm really surprised that this was computationally feasible. Simulation of light through the gratings must have been cheap enough as a function evaluation to train the network.

Lramseyer 4y ago
I would imagine that you generate the desired transform function of a diffractive structure rather than the structure itself, because the structure is ultimately derived from the transform function. Since the transform function is basically a 2D fourier transform and a spatial frequency/phase plot, it's not _that_ computationally costly. Once you settle on functions you like, you then generate and or simulate a diffractive structure and see if it behaves how you expect.

Lramseyer 4y ago

Sort of, I didn't dive too far into the math, but it looks like each diffractive structure is akin a layer of a neural net, which is tuned for a set of spatial frequencies and phases, which when combined (like layers of a neural net) to form recognition of more complex objects. There are a few gotchas in that statement though - for one, I didn't dive too far into the math, and I would assume that the convolutional algorithms as well as the underlying matrix functions may be different. But at the end of the day, you're approximating a complex function using an array of simple functions with different weights and scale factors. The other gotcha is that diffractive structures use monochromatic light, so it's probably not too useful in most normal situations with normal light sources.

SiempreViernes 4y ago

It can do the same sort of computation work any stack of analogue filters can do: it does one thing very fast and if you want something else done you must create those filters first and the frame holding the stack is of no help at all.