Large neural networks spend most computation on floating point tensor multiplications. In this work, we find that a floating point multiplier can be approximated by one integer adder with high precision. We propose the linear-complexity multiplication (L-Mul) algorithm that approximates floating point number multiplication with integer addition operations. The new algorithm costs significantly less computation resource than 8-bit floating point multiplication but achieves higher precision. Compared to 8-bit floating point multiplications, the proposed method achieves higher precision but consumes significantly less bit-level computation. Since multiplying floating point numbers requires substantially higher energy compared to integer addition operations, applying the L-Mul operation in tensor processing hardware can potentially reduce 95% energy cost by elementwise floating point tensor multiplications and 80% energy cost of dot products. We calculated the theoretical error expectation of L-Mul, and evaluated the algorithm on a wide range of textual, visual, and symbolic tasks, including natural language understanding, structural reasoning, mathematics, and commonsense question answering. Our numerical analysis experiments agree with the theoretical error estimation, which indicates that L-Mul with 4-bit mantissa achieves comparable precision as float8 e4m3 multiplications, and L-Mul with 3-bit mantissa outperforms float8 e5m2. Evaluation results on popular benchmarks show that directly applying L-Mul to the attention mechanism is almost lossless. We further show that replacing all floating point multiplications with 3-bit mantissa L-Mul in a transformer model achieves equivalent precision as using float8 e4m3 as accumulation precision in both fine-tuning and inference.
No. But it does potentially mean that either current or future-tweaked GPUs could run a lot more efficiently -- meaning much faster or with much less energy consumption.
To me intuitively using floats to make ultimatelty boolean like decisions seems wasteful but that seemed like the way it had to be to have diffetentiable algorithms.
we used to use Fixed point multiplications (Q Format) in DSP algorithms on different DSP architectures. https://en.wikipedia.org/wiki/Q_(number_format). They used to be so fast and near accurate to floating point multiplications. Probably we need to use those DSPs blocks as part of Tensors/GPUs to realise both fast multiplications & parallelisms.
Then I used it for Llama-3.2-3B-Instruct.F16.gguf and it outputted jibberish. So you would probably have to train and design your model specifically to use this multiplication approximation in order for it to work. Or maybe I'd have to tune the model so that only certain layers and/or operations use the approximation. However the speed was decent. Prefill only dropped from 850 tokens per second to 200 tok/sec on my threadripper. Prediction speed was totally unaffected, staying at 34 tok/sec. I like how the code above generates vpternlog ops. So if anyone ever designs an LLM architecture and releases weights on Hugging Face that use this algorithm, we'll be able to run them reasonably fast without special hardware.
Your kernel seems to be incorrect for 1.75 * 2.5.
From paper we have 1.75 == (1+0.75)*2^0 for 2.5 == (1+0.25)*2^1 so result is
(1+0.75+0.25+2^-4)*2^1 == 4.125 (correct result is 4.375)
Extra. I am not sure if that is clear from paper, but in example of 1.75 * 2.5
we can represent 1.75 also as (1-0.125) * 2. This gives good aproximations for numbers that are close but less than power of 2. This way abs(a*b) in (1+a)*(1+b) is allways small and strictly less than 0.25.
Another example, if we have for example 1.9 * 1.9 then we need to account for overflow in (0.9 + 0.9) and this seems to induce similar overhead as expressing numbers as (1-0.05)*2 .
Extraordinary claims require extraordinary evidence.
Maybe it's possible, but consider that some really smart people, in many different groups, have been working diligently in this space for quite a while; so claims of 95% savings on energy costs _with equivalent performance_ is in the extraordinary category. Of course, we'll see when the tide goes out.
It is a click bait headline the claim itself is not extraordinary.
the preprint from arxiv was posted here some time back .
The 95% gains is specifically only for multiplication operations, inference is compute light and memory heavy in the first place so the actual gains would be far less smaller .
Tech journalism (all journalism really) can hardly be trusted to publish grounded news with the focus on clicks and revenue they need to survive.
I don't think this claim is extraordinary. Nothing proposed is mathematically impossible or even unlikely, just a pain in the ass to test (lots of retraining, fine tuning etc, and those operations are expensive when you dont have already massively parallel hardware available, otherwise you're ASIC/FPGAing for something with a huge investment risk)
If I could have a SWAG at it I would say a low resolution model like llama-2 would probably be just fine (llama-2 quantizes without too much headache) but a higher resolution model like llama-3 probably not so much, not without massive retraining anyways.
I'm not an AI person, in any technical sense. The savings being claimed, and I assume verified, are on ARM and x86 chips. The piece doesn't mention swapping mult to add, and a 1-bit LLM is, well, a 1-bit LLM.
Also,
> Additionally, it reduces energy consumption by 55.4% to 70.0%
With humility, I don't know what that means. It seems like some dubious math with percentages.
They’ve been working on unrelated problems like structure of the network or how to build networks with better results. There have been people working on improving the efficiency of the low-level math operations and this is the culmination of those groups. Figuring this stuff out isn’t super easy.
re: all above/below comments. It's still an extraordinary claim.
I'm not claiming it's not possible, nor am I claiming that it's not true, or, at least, honest.
But, there will need to be evidence that using real machines, and using real energy an _equivalent performance_ is achievable. A defense that "there are no suitable chips" is a bit disingenuous. If the 95% savings actually has legs some smart chip manufacturer will do the math and make the chips. If it's correct, that chip making firm will make a fortune. If it's not, they won't.
It's not their job to make AMD viable, it's AMD's job to make AMD viable. NVIDIA didn't get their position for free, they spent a decade refining CUDA and its tooling before GPU-based crypto and AI kicked off.
As someone who has worked in this space (approximate compute) on both GPUs and in silicon in my research, the power consumption claims are completely bogus, as are the accuracy claims:
> In this section, we show that L-Mul is more precise than fp8 e4m3 multiplications
> To be concise, we do not consider the rounding to nearest even mode in both error analysis and complexity estimation for both Mul and L-Mul
These two statements together are non-sensical. Sure, if you analyze accuracy while ignoring the part of the algorithm that gives you accuracy in the baseline you can derive whatever cherry-picked result you want.
The multiplication of two floating point values if you round to nearest even will be the correctly rounded result of multiplying the original values at infinite precision, this is how floating point rounding usually works and what IEEE 754 mandates for fundamental operations if you choose to follow those guidelines (e.g., multiplication here). But not rounding to nearest even will result in a lot more quantization noise, and biased noise at that too.
> applying the L-Mul operation in tensor processing hardware can potentially reduce 95% energy cost by elementwise floating point tensor multiplications and 80% energy cost of dot products
A good chunk of the energy cost is simply moving data between memories (especially external DRAM/HBM/whatever) and along wires, buffering values in SRAMs and flip-flops and the like. Combinational logic cost is usually not a big deal. While having a ton of fixed-function matrix multipliers does raise the cost of combinational logic quite a bit, at most what they have will probably cut the power of an overall accelerator by 10-20% or so.
> In this section, we demonstrate that L-Mul can replace tensor multiplications in the attention mechanism without any loss of performance, whereas using fp8 multiplications for the same purpose degrades inference accuracy
I may have missed it in the paper, but they have provided no details on (re)scaling and/or using higher precision accumulation for intermediate results as one would experience on an H100 for instance. Without this information, I don't trust these evaluation results either.
Isn't this just taking advantage of "log(x) + log(y) = log(xy)"? The IEEE754 floating-point representation stores floats as sign, mantissa, and exponent -- ignore the first two (you quantitized anyway, right?), and the exponent is just an integer storing log() of the float.
Not quite: It's taking advantage of (1+a)(1+b) = 1 + a + b + ab.
And where a and b are both small-ish, ab is really small and can just be ignored.
So it turns the (1+a)(1+b) into 1+a+b. Which is definitely not the same! But it turns out, machine guessing apparently doesn't care much about the difference.
Feels like multiplication shouldn't be needed for convergence, just monotonicity? I wonder how well it would perform if the model was actually trained the same way.
Yes. I haven't yet read this paper to see what exactly it says is new, but I've definitely seen log-based representations under development before now. (More log-based than the regular floating-point exponent, that is. I don't actually know the argument behind the exponent-and-mantissa form that's been pretty much universal even before IEEE754, other than that it mimics decimal scientific notation.)
I guess that if the bulk of the computation goes into the multiplications, you can work in the log-space and simply sum, and when the time comes to actually do a sum on the original space you can go back and sum.
This has been done for decades in digital circuits, FPGA’s, Digital Signal Processing, etc. Floating point is both resource and power intensive and using FP without the use of dedicated FP processing hardware is something that has been avoided and done without for decades unless absolutely necessary.
Right, the ML people are learning, slowly, about the importance of optimizing for silicon simplicity, not just reduction of symbols in linear algebra.
Their rediscovery of fixed point was bad enough but the “omg if we represent poses as quaternions everything works better” makes any game engine dev for the last 30 years explode.
Not sure there's much to explain. Using integers for math in digital circuits is far more resource and computationally efficient than floating-point math. It has been decades since I did the math on the difference. I'll just guess that it could easily be an order of magnitude better across both metrics.
At basic level it is very simple: A 10 bit bus gives you the ability to represent numbers between 0 and 1 with a resolution of approximately 0.001. 12 bits would be four times better. Integer circuits can do the math in one clock cycle. Hardware multipliers do the same. To rescale the numbers after multiplication you just take the N high bits, where N is your bus width; which is a zero clock-cycle operation. Etc.
In training a neural network, the back propagation math can be implemented using almost the same logic used for a polyphase FIR filter.
Maybe I am just a natural skeptic, but whenever I see a headline that says 'method x reduces y by z%'; but when you read the text it instead says that optimizing some step 'could potentially reduce y by up to z%'; I am suspicious.
Why not publish some actual benchmarks that prove your claim in even a few special cases?
Well, one, because the headline isn't from the researchers, its from a popular press report (not even the one posted here, originally, this is secondary reporting of another popular press piece) and isn't what the paper claims so it would be odd for the paper's authors to conduct benchmarks to justify it. (And, no, even the "up to 95%" isn't from the paper, the cost savings are cited per operation depending on operation and the precision the operation is conducted at, are as high as 97.3%, are based on research already done establishing the energy cost of math operations on modern compute hardware, but no end-to-end cost savings claim is made.)
And, two, because the actual energy cost savings claimed aren't even the experimental question -- the energy cost differences between various operations on modern hardware have been established in other research, the experimental issue here was whether the mathematical technique that enables using the lower energy cost operations performs competitively on output quality with existing implementations when substituted in for LLM inference.
OTOH you have a living proof that an amazingly huge neural network can work on 20W of power, so expecting multiple orders of magnitude in power consumption reduction is not unreasonable.
"The first release of bitnet.cpp is to support inference on CPUs. bitnet.cpp achieves speedups of 1.37x to 5.07x on ARM CPUs, with larger models experiencing greater performance gains. Additionally, it reduces energy consumption by 55.4% to 70.0%, further boosting overall efficiency. On x86 CPUs, speedups range from 2.37x to 6.17x with energy reductions between 71.9% to 82.2%. Furthermore, bitnet.cpp can run a 100B BitNet b1.58 model on a single CPU, achieving speeds comparable to human reading (5-7 tokens per second), significantly enhancing the potential for running LLMs on local devices. More details will be provided soon."
Because as disappointing as modern life is, you need clickbait headlines to drive traffic. You did the right thing by reading the article though, that's where the information is, not the title.
Fair enough, but then I want a way to penalize publishers for abusing clickbait. There is no "unread" button, and there is no way to unsubscribe to advertisement-based sites.
Even on sites that have a "Like / Don't like" button, my understanding is that clicking "Don't like" is a form of "engagement", that the suggestion algorithm are going to reward.
Give me a button that says "this article was a scam", and have the publisher give the advertisement money back. Of better yet, give the advertisement money to charity / public services / whatever.
Take a cut of the money being transfered, charge the publishers for being able to get a "clickbait free" green mark if they implement the scheme.
Track the kind of articles that generate the most clickbait-angry comment. Sell back the data.
Readit News
ABSTRACT
Large neural networks spend most computation on floating point tensor multiplications. In this work, we find that a floating point multiplier can be approximated by one integer adder with high precision. We propose the linear-complexity multiplication (L-Mul) algorithm that approximates floating point number multiplication with integer addition operations. The new algorithm costs significantly less computation resource than 8-bit floating point multiplication but achieves higher precision. Compared to 8-bit floating point multiplications, the proposed method achieves higher precision but consumes significantly less bit-level computation. Since multiplying floating point numbers requires substantially higher energy compared to integer addition operations, applying the L-Mul operation in tensor processing hardware can potentially reduce 95% energy cost by elementwise floating point tensor multiplications and 80% energy cost of dot products. We calculated the theoretical error expectation of L-Mul, and evaluated the algorithm on a wide range of textual, visual, and symbolic tasks, including natural language understanding, structural reasoning, mathematics, and commonsense question answering. Our numerical analysis experiments agree with the theoretical error estimation, which indicates that L-Mul with 4-bit mantissa achieves comparable precision as float8 e4m3 multiplications, and L-Mul with 3-bit mantissa outperforms float8 e5m2. Evaluation results on popular benchmarks show that directly applying L-Mul to the attention mechanism is almost lossless. We further show that replacing all floating point multiplications with 3-bit mantissa L-Mul in a transformer model achieves equivalent precision as using float8 e4m3 as accumulation precision in both fine-tuning and inference.
Presumably there will be a lot of interest.
You still need the GPU parallelism though.
If you're training models with billions of parameters, you're still gonna need that.
Here https://news.ycombinator.com/item?id=41784591 but even before that. It is possibly one of those obvious ideas to people steeped in this.
To me intuitively using floats to make ultimatelty boolean like decisions seems wasteful but that seemed like the way it had to be to have diffetentiable algorithms.
I tried implementing this for AVX512 with tinyBLAS in llamafile.
Then I used it for Llama-3.2-3B-Instruct.F16.gguf and it outputted jibberish. So you would probably have to train and design your model specifically to use this multiplication approximation in order for it to work. Or maybe I'd have to tune the model so that only certain layers and/or operations use the approximation. However the speed was decent. Prefill only dropped from 850 tokens per second to 200 tok/sec on my threadripper. Prediction speed was totally unaffected, staying at 34 tok/sec. I like how the code above generates vpternlog ops. So if anyone ever designs an LLM architecture and releases weights on Hugging Face that use this algorithm, we'll be able to run them reasonably fast without special hardware.Another example, if we have for example 1.9 * 1.9 then we need to account for overflow in (0.9 + 0.9) and this seems to induce similar overhead as expressing numbers as (1-0.05)*2 .
The 95% gains is specifically only for multiplication operations, inference is compute light and memory heavy in the first place so the actual gains would be far less smaller .
Tech journalism (all journalism really) can hardly be trusted to publish grounded news with the focus on clicks and revenue they need to survive.
Right now the only way to gain real knowledge is actually to read comments of those articles.
We have a winner. Glad that came from someone not in my lectures on ML network design
Honestly, thanks for beeting me to this comment
If I could have a SWAG at it I would say a low resolution model like llama-2 would probably be just fine (llama-2 quantizes without too much headache) but a higher resolution model like llama-3 probably not so much, not without massive retraining anyways.
https://github.com/microsoft/BitNet
Also,
> Additionally, it reduces energy consumption by 55.4% to 70.0%
With humility, I don't know what that means. It seems like some dubious math with percentages.
I'm not claiming it's not possible, nor am I claiming that it's not true, or, at least, honest.
But, there will need to be evidence that using real machines, and using real energy an _equivalent performance_ is achievable. A defense that "there are no suitable chips" is a bit disingenuous. If the 95% savings actually has legs some smart chip manufacturer will do the math and make the chips. If it's correct, that chip making firm will make a fortune. If it's not, they won't.
Terrible logic. By a similar logic we wouldn't be using python for machine learning at all, for example (or x86 for compute). Yet here we are.
> In this section, we show that L-Mul is more precise than fp8 e4m3 multiplications
> To be concise, we do not consider the rounding to nearest even mode in both error analysis and complexity estimation for both Mul and L-Mul
These two statements together are non-sensical. Sure, if you analyze accuracy while ignoring the part of the algorithm that gives you accuracy in the baseline you can derive whatever cherry-picked result you want.
The multiplication of two floating point values if you round to nearest even will be the correctly rounded result of multiplying the original values at infinite precision, this is how floating point rounding usually works and what IEEE 754 mandates for fundamental operations if you choose to follow those guidelines (e.g., multiplication here). But not rounding to nearest even will result in a lot more quantization noise, and biased noise at that too.
> applying the L-Mul operation in tensor processing hardware can potentially reduce 95% energy cost by elementwise floating point tensor multiplications and 80% energy cost of dot products
A good chunk of the energy cost is simply moving data between memories (especially external DRAM/HBM/whatever) and along wires, buffering values in SRAMs and flip-flops and the like. Combinational logic cost is usually not a big deal. While having a ton of fixed-function matrix multipliers does raise the cost of combinational logic quite a bit, at most what they have will probably cut the power of an overall accelerator by 10-20% or so.
> In this section, we demonstrate that L-Mul can replace tensor multiplications in the attention mechanism without any loss of performance, whereas using fp8 multiplications for the same purpose degrades inference accuracy
I may have missed it in the paper, but they have provided no details on (re)scaling and/or using higher precision accumulation for intermediate results as one would experience on an H100 for instance. Without this information, I don't trust these evaluation results either.
So it turns the (1+a)(1+b) into 1+a+b. Which is definitely not the same! But it turns out, machine guessing apparently doesn't care much about the difference.
Am I missing something?
Feels like multiplication shouldn't be needed for convergence, just monotonicity? I wonder how well it would perform if the model was actually trained the same way.
You're going to have tolerance on the result anyway, so what's a little more error. :)
https://news.ycombinator.com/item?id=41816598
This has been done for decades in digital circuits, FPGA’s, Digital Signal Processing, etc. Floating point is both resource and power intensive and using FP without the use of dedicated FP processing hardware is something that has been avoided and done without for decades unless absolutely necessary.
Their rediscovery of fixed point was bad enough but the “omg if we represent poses as quaternions everything works better” makes any game engine dev for the last 30 years explode.
At basic level it is very simple: A 10 bit bus gives you the ability to represent numbers between 0 and 1 with a resolution of approximately 0.001. 12 bits would be four times better. Integer circuits can do the math in one clock cycle. Hardware multipliers do the same. To rescale the numbers after multiplication you just take the N high bits, where N is your bus width; which is a zero clock-cycle operation. Etc.
In training a neural network, the back propagation math can be implemented using almost the same logic used for a polyphase FIR filter.
Why not publish some actual benchmarks that prove your claim in even a few special cases?
And, two, because the actual energy cost savings claimed aren't even the experimental question -- the energy cost differences between various operations on modern hardware have been established in other research, the experimental issue here was whether the mathematical technique that enables using the lower energy cost operations performs competitively on output quality with existing implementations when substituted in for LLM inference.
Should be able to go more efficient as the brain has other constraints such as working at 36.7 degrees C etc.
"The first release of bitnet.cpp is to support inference on CPUs. bitnet.cpp achieves speedups of 1.37x to 5.07x on ARM CPUs, with larger models experiencing greater performance gains. Additionally, it reduces energy consumption by 55.4% to 70.0%, further boosting overall efficiency. On x86 CPUs, speedups range from 2.37x to 6.17x with energy reductions between 71.9% to 82.2%. Furthermore, bitnet.cpp can run a 100B BitNet b1.58 model on a single CPU, achieving speeds comparable to human reading (5-7 tokens per second), significantly enhancing the potential for running LLMs on local devices. More details will be provided soon."
Even on sites that have a "Like / Don't like" button, my understanding is that clicking "Don't like" is a form of "engagement", that the suggestion algorithm are going to reward.
Give me a button that says "this article was a scam", and have the publisher give the advertisement money back. Of better yet, give the advertisement money to charity / public services / whatever.
Take a cut of the money being transfered, charge the publishers for being able to get a "clickbait free" green mark if they implement the scheme.
Track the kind of articles that generate the most clickbait-angry comment. Sell back the data.
There might a business model.
Reader: do the moral thing and read the article, not just the title
How is that balanced.