[HN Gopher] Powerful supercomputer can now run on light instead ...
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Powerful supercomputer can now run on light instead of electric
current
Author : mardiyah
Score : 190 points
Date : 2021-12-27 12:34 UTC (1 days ago)
(HTM) web link (www.techradar.com)
(TXT) w3m dump (www.techradar.com)
| neatze wrote:
| Seems like you can try it out[1], I find this a bit funny that it
| is easier to get trail access to quantum CPU and light based GPU,
| but for Cerebras and Graphcore trial access you need spend
| thousands of dollars.
|
| [1]https://lighton.ai/cloud/
| 1MachineElf wrote:
| >According to LightOn, its Appliance can reach a peak performance
| of 1.5 PetaOPS at 30W TDP and can deliver performance that 8 to
| 40 times higher than GPU-only acceleration.
|
| Impressive!
|
| LightOn hasn't received much discussion on here before. Some
| links have been submitted, and this is the only one I could find
| comments on: https://news.ycombinator.com/item?id=27797829
| fsh wrote:
| From the website of the manufacturer [1] it appears that the
| co-processor is essentially an analog computer for matrix-
| vector multiplications. I am quite sceptical about the accuracy
| and value range of the computations. Even puny single-precision
| floating point operations are accurate to something like 7
| decimal digits and have a dynamic range of hundreds of dB.
| According to the spec sheet, the appliance only uses 6-bit
| inputs and 8-bit outputs, so the relative errors are probably
| on the percent level. This makes it hard to believe that any
| signal will propagate through something like a DNN without
| completely drowning in noise.
|
| [1] https://lighton.ai/lighton-appliance/
| bjornsing wrote:
| If there's too much noise just lower the dropout probability
| from 50 to 30%. ;)
|
| Joking aside, it is interesting how much noise and
| quantization these neural networks can work with. I think
| there's a lot of room for low precision noisy computation
| here.
| orlp wrote:
| > Even puny single-precision floating point operations are
| accurate to something like 7 decimal digits and have a
| dynamic range of hundreds of dB. According to the spec sheet,
| the appliance only uses 6-bit inputs and 8-bit outputs, so
| the relative errors are probably on the percent level. This
| makes it hard to believe that any signal will propagate
| through something like a DNN without completely drowning in
| noise.
|
| Maybe you aren't aware, but half-precision (16 bit float) is
| already well-established in the AI community:
| https://en.wikipedia.org/wiki/Bfloat16_floating-point_format.
| In context single-precision isn't all that puny!
|
| And there have already been successful experiments with
| stronger quantization, like 8-bit neural nets, or even 1-bit
| (!) neural nets. There is a lot of evidence that neural
| networks can be very resilient to quantization noise.
| bodhiandphysics wrote:
| It's so annoying!!!! I work in computer graphics and
| scientific computation and it's getting hard to get gpus
| with adequate double performance.
| chillee wrote:
| You might be interested in the upcoming AMD Mi200 GPUs,
| which have 96 teraflops of fp64 performance.
| bodhiandphysics wrote:
| Unfortunately, I need cuda (for now)
| sudosysgen wrote:
| With some tweaking, I've had sucess running CUDA code
| with AMD's HIP framework. You'll need to do some changes
| probably.
| simplestats wrote:
| I think it's hilarious. when I was in school,
| microprocessors were 8-bit. Then as the world got
| digitized it was 16-bit microprocessors. A least in my
| narrow world. Then 32 bit and floats came along and
| finally double floats. Each step was a big product effort
| and launch we sell as better technology. And just as we
| are finally got past the need to always make both 32 and
| 64 bit versions of everything, we turn around and head
| back down. Though I saw someone (Qualcomm?) with a press
| release about their next gen microprocessor supporting 32
| bit floats! Not sure if it counts as another U-turn or
| they're just a straggler.
| wtallis wrote:
| I think you may be improperly conflating address or
| pointer width with the data types used for integer or
| floating-point arithmetic--we had floats up to 80 bits
| with "16-bit" x86 processors. Nobody's moving backwards
| in terms of pointer size. And any history of the
| progression of bit widths is incomplete without
| mentioning the SIMD trend that PCs have been on since the
| mid-90s, starting with 64-bit integer vectors and
| culminating in today's 512-bit vector instructions that
| re-use those original 64-bit vector registers as mask
| registers.
|
| I don't think there's any point at which PCs have ever
| abandoned 8-bit and 16-bit data types, or ever appeared
| to be on a trajectory to do so. We've just had some
| shifts over the years of what kinds of things we use
| narrower data types for.
| bee_rider wrote:
| I think we'll just have to embrace it. Anyway, dealing
| with reduced precision is more fun that throwing bits at
| the problem.
| ISL wrote:
| I'd be real surprised if the neurons in our brains have
| ADC-equivalents better than ~4 bits.
| tgv wrote:
| True, but ANNs are nowhere near as good as our brains,
| nor do they operate in the same way.
| xwolfi wrote:
| I think you missed the fact we were talking about neural
| network, not an animal brain self replicating and
| branching and competing with itself for billions of years
| until it becomes aware of itself. Give us the the same
| time.
| [deleted]
| Retric wrote:
| The earliest and simplest brains where still useful. Even
| insects can fly around in 3D space, I doubt you need
| something as complicated as a mouse brain to run a self
| driving car let alone a drone.
| gnatman wrote:
| Insects also crash into stuff constantly!
| ben_w wrote:
| I'm not sure how much it matters given this thread looks
| like it's going off on several successive tangents, but
| the important (and hard) thing with a self-driving car is
| making sure it doesn't hit stuff, not the actual driving
| part.
|
| And drones, trivially agree: _Megaphragma mymaripenne_
| has 7400 neurones, compared to the 71 /14 million in a
| house mouse nervous system/brain.
| robwwilliams wrote:
| And to stay on this odd tangent:
|
| Best estimate I have for total cell numbers in mouse
| brain--about 75 million neurons and 35 million other cell
| types. This estimate is from a 476 mg brain of a C57BL/6J
| case--the standard mouse used by many researchers.
|
| Based on much other work with discrete neuron populations
| the range among different genometypes of mice probable
| +/- 40%.
|
| for details see: www.nervenet.org/papers/brainrev99.html
|
| Expect many more (and I hope better) estimates soon from
| Clarity/SHIELD whole brain lighsheet counting with Al
| Johnson and colleagues at Duke and team at Life Canvas
| Tech.
| thesz wrote:
| These 1-bit-per-coefficient neural nets need pretty good
| floating point implementation to train them. From what I
| remember, they are trained with rounding - basically, a
| floating point weight gets rounded to -1, 0 or 1 and
| computed floating point gradient is added to a floating
| point weight.
|
| Inference is cheap, training is not.
| tdrdt wrote:
| But arent there other applications where this is ok?
|
| For example path tracing (ray tracing) doesn't need to be
| very accurate because multiple samples per pixel are used.
|
| A gaming card that uses less power is very welcome in laptops
| for example.
| moonchrome wrote:
| What do you mean? What kind of worlds can you represent
| with 8 bits units ? Some small blocky voxel box ?
| tdrdt wrote:
| I mean inacurate vector math
| moonchrome wrote:
| But that is what I'm saying if your vectors are reduced
| to 8 bit scalar components you can represent a
| 256x256x256 worth of detail in the world (doesn't need to
| be linear but still really limited details) ?
| kortex wrote:
| It's not a transmission line though, SNR does not apply in
| the same way. It's more like CMOS where the signal is
| refreshed at each gate. Each stage of an ANN applies some
| weight and activation. You can think of each input vector as
| a vector with a true value plus some noise. As long as that
| feature stays within some bounds, it is going to represent
| the same "thought vector".
|
| It may require some architecture changes to make training
| feasible, but it's far from a nonstarter.
|
| And that is only considering backprop learning. The brain
| does not use backprop, and has way higher noise levels.
| dahart wrote:
| I think the parent was referring to the same noise that you
| are, compute precision, not transmission, and was
| suggesting that perhaps it won't easily stay within bounds
| due to the fact that some kinds of repeated calculations
| lose more precision at every step.
|
| Maybe it's application dependent, maybe NNs or other
| matrix-heavy domains can tolerate low precision much more
| easily than scientific simulations. It certainly wouldn't
| surprise me if these "LightOPS" processors work well in a
| narrow range of applications, and won't improve or speed up
| just anything that needs a matrix multiply.
| robert_tweed wrote:
| For a few seconds I thought it was Lite-On, best known for
| their cheapo CD/DVD drives. Seems to be completely unconnected
| though.
| Datagenerator wrote:
| Brings back memories of the Plextor automatic duplicator
| robot we had in company back in the nineties. Great times
| inasio wrote:
| I've never heard of LightOn, and wish the website had a bit
| more concrete info on the specifics of the coprocessor, but I
| am somewhat familiar with a similar photonic coprocessor made
| by NTT (the Coherent Ising Machine). It's still in the research
| stage, the logic uses interferometry effects, and requires
| kilometers of fiber optic cables. Interestingly, there is a
| simulator based on mean field theory that runs on GPUs and
| FPGAs(*) that can solve some problems (e.g. SAT) with close to
| state of the art performance.
|
| (*) disclosure: my company helped build the simulator
| dasudasu wrote:
| There are other startups in the space that do it in
| semiconductors. Look up Lightelligence and Lightmatter for
| instance.
| zapdrive wrote:
| Nice. Can't wait for the new light based GPUs, all being
| grabbed by greedy crypto miners and me still using my 6 year
| old graphics card!
| JohnJamesRambo wrote:
| Relief is on the horizon. Ethereum should switch to proof of
| stake in June 2022 and you are about to see an unholy torrent
| of used GPUs hit the market. I would expect you can pick up
| any you like for peanuts then.
| demux wrote:
| Ethereum PoW won't immediately disappear, and I'm sure
| bitcoin folk will be all too happy to grab those extra GPUs
| zapdrive wrote:
| I have been hearing "Ethereum is switching to proof of
| stake in a few months" for at least 6 years now. I don't
| think it's going to ever happen.
| mikewarot wrote:
| The only actual hardware description I could find was in this
| arXiv link, where you have a laser that is spread then put
| through a light gate chip (as found in projectors), a random
| mask, then to a CCD camera. This does random multiplies, in
| parallel, which somehow prove useful.
|
| I fail to see how it actually does matrix math.
|
| https://arxiv.org/abs/1609.05204
| [deleted]
| daralthus wrote:
| It does random projections [1] which is really useful for
| dimensionality reduction.
|
| [1] https://en.wikipedia.org/wiki/Random_projection
| 14 wrote:
| I remember hearing about Lifi [1] years ago and thinking we would
| see it everywhere but this has not been the case. I wonder what
| has held it back. Like this super computer Lifi promised
| unmatched speeds that wifi can not do. Very neat to see the field
| is still advancing.
|
| [1] https://lifi.co/lifi-vs-wifi/
| tomlue wrote:
| there was a ted talk [1] that made me think lifi would be take
| off much faster than it has.
|
| [1]https://www.ted.com/talks/harald_haas_wireless_data_from_eve
| ...
| crate_barre wrote:
| How could LiFi be truly wireless if anything can obstruct the
| path of light? How's my phone in my pocket going to get
| connection?
| croes wrote:
| If you don't need a cable it's wireless notwithstanding any
| other disadvantages
| dmm wrote:
| Why restrict yourself to visible light? There are frequencies
| of em waves that would easily penetrate your jeans:
| https://en.wikipedia.org/wiki/Gamma_ray
| [deleted]
| croes wrote:
| Isn't the use of visible light the whole point LiFi?
| Denvercoder9 wrote:
| Usually we go to the lower-energy, longer-wavelength part
| of the spectrum for applications like this, since gamma
| rays and the high-energy, short-wavelength part of the
| spectrum is very hard to control and gives you cancer.
| causality0 wrote:
| Keeping a multi-watt transmitter of ionizing radiation in
| your pocket is a very bad idea.
| ben_w wrote:
| Or indeed a single-milliwatt transmitter, if it's in your
| pocket for more than an hour or so per lifetime.
| causality0 wrote:
| I see this "cell phones will use x-rays and gamma rays in
| the future" claim often enough that I wish an expert in
| the field would write an article on just how bad the
| effects would be.
| up6w6 wrote:
| It seems that light reflected off walls can achieve up to 70
| Mbit/s in a controlled environment. But yeah, it's still hard
| to think about direct applications in our lives.
|
| https://en.wikipedia.org/wiki/Li-Fi
|
| https://www.abc.net.au/radionational/programs/scienceshow/th.
| ..
| 14 wrote:
| there are many use cases that don't require you to be
| connected 24/7. You could while driving under a street light
| download a movie in seconds. Then go on your way loading your
| cars infotainment with maps and several movies for your kids
| in the back or whatever. I haven't looked into the tech in
| years but the promised of faster downloads and a city wide
| array of street lights made it seem like the future.
| zbrozek wrote:
| Aperture fouling (dirt / grime) seems like it would make
| such a service flaky. Aside from needlessly low data caps,
| the cell network is pretty great for road trip
| connectivity. High bandwidth intermittent connectivity
| would be nice for self-driving car sensor log offload.
|
| Inside my home it would be cool to have 10 gbps to my
| laptop, but I don't have a real use case where that's
| meaningfully better than the 500-800 mbps that I already
| get with WiFi.
| 14 wrote:
| The sensor could be mounted behind your windshield which
| we already have windshield wash built into every car and
| be cleaned effortlessly. I don't see that being an issue.
| zbrozek wrote:
| Maybe, but the other side also needs to be cleaned. And
| the car side TX won't be anywhere near as bright as a
| street lamp (and probably IR) and will be more
| vulnerable.
|
| As you point out, all of this is likely surmountable,
| but... why bother if the status quo is serving the use
| case?
| bogwog wrote:
| > pretty great for road trip connectivity
|
| Until people start getting seizures while driving from
| all the flashing lights
| 14 wrote:
| The flashing happens so fast it is invisible to human
| eye. LED lights already do with with pulse width
| modulation to make them as efficient as they are and it
| is not an issue.
| zbrozek wrote:
| Correct, though I was actually referring to the existing
| cell network as great for road trips.
| dekhn wrote:
| I can see LEDs flashing out of the corner of my eye when
| it's moving quickly, it's really obnoxious.
| causality0 wrote:
| That page is amateurish and riddled with absurd statements,
| like the claim visible light travels faster than radio waves.
| It also claims LiFi offers speeds "100 times faster than wifi"
| but their thousand dollar router can only do 100Mbps. To add
| insult to injury it rips off the Wi-Fi trademark logo as well.
|
| There may be a market for visible light networking but LiFi is
| total garbage.
| crate_barre wrote:
| Would this generate less heat? Heat is still a bottleneck in some
| ways right? What about size? Can we get smaller?
|
| Would we need semiconductors anymore?
| adgjlsfhk1 wrote:
| heat is just power. 10x less power is 10x less heat.
| foobarian wrote:
| 10x less power is 10x more gear I can run off the same outlet
| :-)
| goldenkey wrote:
| Indeed. All electrical devices are just space heaters that do
| something logical with the electricity while it's heating up
| the wires :-)
| amelius wrote:
| https://en.wikipedia.org/wiki/Adiabatic_circuit
| ww520 wrote:
| I'm not super well versed on this topic. But the basic physics of
| photon and electron make light a poor source for computing
| compared to electricity. Photons don't interact with each other
| much when crossed, while electrons interfere each other greatly.
| It's really difficult to build logic gates out of photons while
| electrons work great with semiconducting materials to build
| gates.
|
| Light is good for communication due to its non-interfering nature
| to pump up the bandwidth. There's a saying light is great for
| data transmission while electricity is great for computing.
|
| So when people claim making supercomputer out of optical
| computing, take it with a grain of salt.
| aidenn0 wrote:
| Photons may not interact with themselves much, but they
| interact with other materials in significant and useful ways,
| and there are plenty of materials that change their optical
| properties in response to an electric field (which can be
| either electronic or optical in origin, given that light,
| particularly coherent light can have fairly strong electric
| fields).
|
| There are millions of things that an electronic digital
| computer can do that are unlikely to be replaced by photonics,
| but a hybrid approach may offer advantages in computing
| specific things. As we have slowed down getting perf/watt
| advantages from shrinking processes, more and more specialized
| hardware has been used for performing calculations. It's not
| that far-fetched to think that photonics might have a niche
| where it has performance advantages.
| ww520 wrote:
| You're right that photons interact with many materials.
| However, few exhibit semiconducting properties that's useful
| for building logic gates.
|
| Silicon has a kind of perfect energy band gap for its valence
| band electrons jumping to conducting band free elections to
| allow electricity flow. The gap is not too small to introduce
| ambiguity or too big to require too much energy to move from
| non-conductive to conductive state. Photonics needs to find a
| semiconducting material/alloy that beats silicon to be a
| viable option.
|
| Most research in building logic gate with light is a
| combination of light and electricity. The most promising
| recently is using Josephson junction in a superconducting
| electric current loop. A photon hitting the loop adds energy
| to the superconducting current. With enough energy the
| current becomes critical current, which moves the Josephson
| junction from 0 voltage to a voltage. The raised voltage
| gives off the energy and the current falls back to non-
| critical. Continuous photons hitting the loop causes the
| Josephson junction to have an extremely high frequency AC
| voltage. That's a photon controlled gate.
|
| But the research is still really early and it requires low
| temperature superconductivity. It's still a long way to be
| competitive in reality.
| krasin wrote:
| As other commenter said, the magic happens not just between
| photons, but between photons and non-linear optical materials,
| in which these photons travel.
|
| While not directly related to computing, I was fascinated to
| learn that lasers routinely use crystals to cut wavelength of
| the light by half ([1], [2]).
|
| 1. https://en.wikipedia.org/wiki/Second-harmonic_generation
|
| 2.
| https://en.wikipedia.org/wiki/Potassium_dideuterium_phosphat...
| ww520 wrote:
| That's true but so far none of those materials found, to be
| competitive with electricity+silicon.
| faeyanpiraat wrote:
| There is an upcoming Veritasium video about the "comeback of
| analogue computers".
|
| Part one (teaser): https://www.youtube.com/watch?v=IgF3OX8nT0w
| sshlocalhost98 wrote:
| Yup, I saw it, what is he actually trying to say ? How can
| analog computer supercede digital, analogue is made too
| specific for only 1 task
| JumpCrisscross wrote:
| We have _tonnes_ of computing power dedicated to repeatedly
| solving a simply-parameterised problem.
| rawoke083600 wrote:
| Stupid question... with todays memory capacities....At what
| limit/size do we stop using matrix-ops and simply use
| lookup tables todo 'matrix-math' ?
| adgjlsfhk1 wrote:
| TLDR is you can't. For a very simple example, storing the
| products of all 3x3 matrices * length 3 vectors in
| Float16 precision would take 2^193 bytes (which is
| obviously impractical).
| jeffbee wrote:
| Not a stupid question. Economically, memory density will
| hit a brick wall soon. Developers should prefer to waste
| time and save space, since parallel computation will not
| hit a similar limit in the foreseeable future. Memory-to-
| core ratio is going to be falling.
| aidenn0 wrote:
| Your CPU has dedicated circuitry for performing CRC32 and AES
| rounds. That's as specific as any analogue computer...
| kortex wrote:
| If that "1 task" happens to be performing matrix
| multiplication (or even merely fused multiply add), you can
| do a heck of a lot with that. You still need digital
| circuitry to support the IO, but the key idea is doing linear
| algebra in a way that is faster and/or generates less heat
| per unit compute.
| magicalhippo wrote:
| On a related note, the Huygens Optics channel on YouTube
| published a video[1] earlier this year on the attempts to make
| optical logic gates.
|
| He didn't get as far as making working devices, work in progress,
| but interesting still IMHO. He also has a lot of other great
| videos about optics.
|
| [1]: https://www.youtube.com/watch?v=pS1zAAD1nXI
| vmception wrote:
| There are some people that view these as a solution to Proof of
| Work energy use
|
| I've been researching OPUs for this purpose, as in, the concept
| of optical processors only came to my attention because of the
| people looking for an edge in mining and energy use.
|
| From what I can tell, it could only be a stopgap or decade long
| solution to PoW, as people would just hoard these over time till
| the energy use was the same
|
| But any slowdown is good
|
| Good for sellers of OPUs though
| adgjlsfhk1 wrote:
| Light based computers work best on linear operations. They are
| extremely unlikely to work well for computing hashes.
| vmception wrote:
| Right well, thats why there is a new hashing algorithm. And
| they want other energy heavy cryptocurrencies to switch to
| it.
|
| Basically there is a whole row going on in the far far
| corners of crypto land, where some Cambridge and Columbia
| university alumni have made a new hashing algorithm
| (HeavyHash) that is heavy on linear operations specifically
| so that it would theoretically have an advantage on light
| based computers and be a sustainability solution [for now].
|
| They stood up an example project back in May and forgot about
| it ("optical bitcoin", oBTC), but people kept mining it. Just
| on GPUs and FPGAs, as the low power better processors don't
| exist yet so there isn't really anything different at the
| moment. Because these are students with no funding, the
| management is very weak.
|
| There is at least one fork of that project that has better
| management ("photonic bitcoin", pBTC). But they are waiting
| for OPUs to exist at all, as there are a variety of vaporware
| companies out there with massive funding.
|
| HeavyHash itself is being used in more and more other newly
| launched cryptocurrencies. Hoping for OPUs to become
| available to actually make their networks different than
| others.
|
| They all so far only aspire to be examples for other major
| energy consuming cryptocurrencies we've heard of to switch
| to. The university students had submitted a proposal (BIP) to
| Bitcoin-core, and that slow moving network typically needs
| real world examples and fear of missing out for consensus to
| shift.
| simias wrote:
| I don't see how that adds up, unless production of these light
| computers is extremely constrained they are just going to be
| produced en masse if they provide an edge for PoW mining, then
| you'll just have many more computers using the same amount of
| energy. And if the supply is constrained in such a way that
| only a tiny amount of people have access to the technology it
| just means that you have a centralized mining pool that can
| easily perform a 51% attack.
|
| It's always a zero-sum game in the end. The only way to "fix"
| PoW is to get rid of it.
| vmception wrote:
| yeah my post covered that, with much more brevity. read it
| again, slowly, specifically the third line.
| vlovich123 wrote:
| I think the contention is around that it could even be a 10
| year stopgap. I too think it would be much shorter - a
| couple of years at most.
| vmception wrote:
| ah okay so some of us are are agreeing about the limited
| utility.
|
| I mostly think the production and distribution would be
| constrained for the level of demand out there.
| simias wrote:
| Indeed, I should have made that clearer. 10 years is what
| separates the iphone 1 and the iphone 8, or the
| PlayStation and the PlayStation 3. If there's a
| breakthrough in computing technology it'll be everywhere
| within a couple of years IMO, and miners will be among
| the first ones served because they're willing to pay
| above market price and in bulk (see the GPU situation at
| the moment).
| danlugo92 wrote:
| > it just means that you have a centralized mining pool that
| can easily perform a 51% attack.
|
| Miners do not ultimately decide what blocks get into the
| blockchain or not, full nodes[0] do.
|
| Here's a collection of 8 articles explaning who (if anyone)
| controls Bitcoin and why miners are not who are in control:
|
| https://endthefud.org/control
|
| [0] ~$200 of hardware, and there are about 12k of them right
| now.
| simias wrote:
| I don't understand the relevance of your articles. What
| would nodes have to do with the issue of who creates the
| nodes? Why would nodes reject valid blocks arbitrarily? Why
| would it be an improvement?
|
| I'm talking about a situation where a small group of people
| would have access to exclusive technology that would let
| them mine blocks faster than the rest of the miners with no
| way for others to compute without losing money. Nodes are
| irrelevant here unless they decide to arbitrarily reject
| valid blocks coming for certain miners because they'd deem
| them "unfair competition", but that's a huge can of worms.
| Who decides who goes on the list? Based on what? Could it
| not be trivially worked around?
| blihp wrote:
| The whole point of PoW is that it requires a given amount of
| effort at a given level of difficulty to maintain a given level
| of production. (i.e. it's a function of the capital cost of the
| equipment and the operational cost of running it) All else
| being equal, if the amount of effort to produce a given result
| is reduced it will result in an increased level of difficulty
| netting out to a similar level of energy use.
|
| This is the reason that Bitcoin, for example, keeps ratcheting
| up the difficulty: to counteract the increased performance of
| CPUs, then GPUs, then FPGAs and finally ASICs over time. It's
| an arms race that you can't 'win' for any extended period of
| time since the difficulty is not a constant, but rather
| determined by the desired level of production.
| mrobot wrote:
| Some info on China's Jiuzhang 2
|
| https://interestingengineering.com/chinas-new-quantum-comput...
| rahimiali wrote:
| The lighton device accelerates random linear projections. Its
| input is a vector x and its output is a vector W*x, where W is a
| fixed random matrix. This is useful for a class of machine
| learning algorithms, but not frequently used in deep learning.
| sudosysgen wrote:
| Can you not decompose general matrix multiplication into the
| sum of vector matrix multiplications?
| [deleted]
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