> We measure the actual symbol distribution of 29 ternary LLM models and find that zeros account for up to 51.5% of all weights. Motivated by this finding, we introduce BITCOS, a simple distribution-adaptive layout
I honestly assumed that's how they already work. I have to admit that I even explained it like that to a friend. Why on earth wouldn't you design it like that from the start (talking about the adaptive, not the measure part; just sacrifice a few bits to clarify your encoding and save a ton of bits)?
By “work out” you mean no accuracy degradation? That’s a big ask - currently we can barely quantize to dynamic fp4 with small block size - still not completely lossless on all benchmarks.
QAT, which bitnet training is a form of, helps a ton in preserving accuracy at such low bits per parameter. There are also better quantization approaches that try to preserve the most sensitive weights† but are computationally expensive and so not typically done. Another complementary option is, if the model is fast enough, we should be able to push up correctness by self-consistency voting at close to T=1. Smart/fast Zero-shot classifiers like the recent Jev could help with aggregation across answers too, extending applicability.
†Every paper I've read estimates the average information content of transformer LLMs at about 3-4 bits per parameter. Curiously, biological synapses are also estimated to be about 4-5 bits per synapse, possibly a bit lower.
the average information content of transformer LLMs at about 3-4 bits per parameter
The problem is that 4-bit block-wise quantization does not guarantee preserving 4 bits of useful information per parameter - not even on average. It simply assigns one of 16 quantization levels to each weight, with the whole block sharing the same scale/range.
How efficiently those 16 levels preserve the model’s information depends on the weight distribution, block size, range/clipping strategy, outliers, and which weights are actually important. Some weights may be represented almost exactly, while others lose much of their useful information.
A simple example is an outlier: if you choose the range to preserve a very large weight, much of the 16-level dynamic range is spent on that outlier, leaving coarse resolution for all the smaller weights in the block. So 4 bits of storage does not imply 4 bits of useful information preserved. Yes, QAT helps, but usually at the cost of learning efficiency. It takes longer to train a model to the same quality when using less precision, and sometimes we simply cannot get to the same quality level with not enough precision in the right places.
Another problem in quantization is that we don't really know which weights are sensitive - we can compute various sensitivity metrics, and some of these metrics will correlate with accuracy on some benchmarks, but not on others.
Another complementary option is, if the model is fast enough, we should be able to push up correctness by self-consistency voting at close to T=1. Smart/fast Zero-shot classifiers like the recent Jev could help with aggregation across answers too, extending applicability.
I'm not convinced by this argument - if such a method improves accuracy of a degraded quantized model, then it could in theory also help non-degraded full precision model. And if so, then we are back to square one, because this composite model will then get degraded due to quantization (baseline has improved!)
We do know one thing - increasing the size of the model usually makes it more robust to quantization. If going from 8 bits to 2 bits speeds things up by a factor of, say, 4x, then if we double the size of the model, we might still end up with an overall speedup. Finding this balance might become a hot area of research.
That's what I meant - we are currently use fp4 formats for training, and we cannot quite get away with that, despite dynamic quant and small block size - we still have to use quite a bit of higher precision (fp8 or even fp16) in various model components.
I might still be misunderstanding what you are saying, but bitnet also keeps high precision latent weights during training. The optimizer updates those, while the weights used in the forward pass are quantized to ternary values.
PTQ and vector quantization aren’t used for this because part of the point of ternary LLMs is to make them faster. In a ternary LLM every weight is an add, subtract, or no-op so it is fast on CPU.
If you’re just using a code book to reconstruct a f16 model the only savings you can get are in sending it over the wire.
in the case of large language models, the wire is the communication of your parameters between your layers of memory that is often the bottleneck. To do a forward pass, you need to use all parameters once, and so the communication between the compute and the storage is the bottleneck, and that bottleneck is also a bunch of wires.
If you want sub-2 bit llm, get one that’s already trained in higher precision, and compress it with something like YAQA/QTIP with finetuning or PV-tuning + AQLM/HIGGS
Only a presence bitmap? If we're contemplating packing schemes I'm tempted to write a paper that uses arithmetic coding to squeeze out a few more centi-bits.
Agreed. One possible objection might be that they need fast random access to weights, but I skimmed parts of the paper and it looks like they process 128 entries at a time, which to me sounds like it should be amenable to better compression: short enough that better compression results could still be efficiently cached in faster local RAM, long enough that better compression would save useful amounts of memory per block.
It also means you can read them faster, more parameters per second during an inference which tends to be memory bandwidth limited on most systems. Thus faster inferences
sounds like a perfect fit for ASIC-optimized models (where matrix ops could be supported directly in BITCOS format, potentially) & achieving record power efficiency for on-device inference.
And it looks like per [0], a model needs only ~30% more weights to be at comparable quality, if quantization-aware training is done...
Why not just use an 8-bit LUT to encode the 256 most common ternary vectors with 6 components. That means of the possible 729 possible such vectors, you can only represent 256 different ones. You have to do more aggressive rounding, but at least the scheme is very simple to decompress and stream.
I think the weights are iid distributed, so all 729 patterns will be roughly equally likely. That doesn't make this a bad idea though -- it just means there's no point trying to select the most common 256 to keep, since any 256 will be roughly as good.
Thank you for sharing this. I like to test out running LLM's on edge computing with limited RAM and GPU/CPU so this research will have practical implications on my activities. I also appreciated how the authors formulated 1.58 (it's log_2(3)) because that was embarrassingly confusing for me when I was first introduced to ternary LLM's.
> We measure the actual symbol distribution of 29 ternary LLM models and find that zeros account for up to 51.5% of all weights. Motivated by this finding, we introduce BITCOS, a simple distribution-adaptive layout
I honestly assumed that's how they already work. I have to admit that I even explained it like that to a friend. Why on earth wouldn't you design it like that from the start (talking about the adaptive, not the measure part; just sacrifice a few bits to clarify your encoding and save a ton of bits)?
So they get down from 1.58 to 1.48 bits per weight by exploiting the fact that actual weights in practice are 0 51% of the time. Neat.
If ternary llms work out and are baked into hardware as custom silicon I bet they'll be shockingly efficient.
By “work out” you mean no accuracy degradation? That’s a big ask - currently we can barely quantize to dynamic fp4 with small block size - still not completely lossless on all benchmarks.
QAT, which bitnet training is a form of, helps a ton in preserving accuracy at such low bits per parameter. There are also better quantization approaches that try to preserve the most sensitive weights† but are computationally expensive and so not typically done. Another complementary option is, if the model is fast enough, we should be able to push up correctness by self-consistency voting at close to T=1. Smart/fast Zero-shot classifiers like the recent Jev could help with aggregation across answers too, extending applicability.
†Every paper I've read estimates the average information content of transformer LLMs at about 3-4 bits per parameter. Curiously, biological synapses are also estimated to be about 4-5 bits per synapse, possibly a bit lower.
the average information content of transformer LLMs at about 3-4 bits per parameter
The problem is that 4-bit block-wise quantization does not guarantee preserving 4 bits of useful information per parameter - not even on average. It simply assigns one of 16 quantization levels to each weight, with the whole block sharing the same scale/range.
How efficiently those 16 levels preserve the model’s information depends on the weight distribution, block size, range/clipping strategy, outliers, and which weights are actually important. Some weights may be represented almost exactly, while others lose much of their useful information.
A simple example is an outlier: if you choose the range to preserve a very large weight, much of the 16-level dynamic range is spent on that outlier, leaving coarse resolution for all the smaller weights in the block. So 4 bits of storage does not imply 4 bits of useful information preserved. Yes, QAT helps, but usually at the cost of learning efficiency. It takes longer to train a model to the same quality when using less precision, and sometimes we simply cannot get to the same quality level with not enough precision in the right places.
Another problem in quantization is that we don't really know which weights are sensitive - we can compute various sensitivity metrics, and some of these metrics will correlate with accuracy on some benchmarks, but not on others.
Another complementary option is, if the model is fast enough, we should be able to push up correctness by self-consistency voting at close to T=1. Smart/fast Zero-shot classifiers like the recent Jev could help with aggregation across answers too, extending applicability.
I'm not convinced by this argument - if such a method improves accuracy of a degraded quantized model, then it could in theory also help non-degraded full precision model. And if so, then we are back to square one, because this composite model will then get degraded due to quantization (baseline has improved!)
We do know one thing - increasing the size of the model usually makes it more robust to quantization. If going from 8 bits to 2 bits speeds things up by a factor of, say, 4x, then if we double the size of the model, we might still end up with an overall speedup. Finding this balance might become a hot area of research.
Well, you could train directly at this bitrate.
You are conflating post training quantization and low bit training.
That's what I meant - we are currently use fp4 formats for training, and we cannot quite get away with that, despite dynamic quant and small block size - we still have to use quite a bit of higher precision (fp8 or even fp16) in various model components.
I might still be misunderstanding what you are saying, but bitnet also keeps high precision latent weights during training. The optimizer updates those, while the weights used in the forward pass are quantized to ternary values.
Ternary quantization does not make any sense. Vector quantization and trellis based methods are better in this region for PTQ.
PTQ and vector quantization aren’t used for this because part of the point of ternary LLMs is to make them faster. In a ternary LLM every weight is an add, subtract, or no-op so it is fast on CPU.
If you’re just using a code book to reconstruct a f16 model the only savings you can get are in sending it over the wire.
And storing it in memory. Memory is expensive.
which is important though since sending it across the wire over and over and over is actually the main bottleneck.
Wire typically means internet connection, and it’s hardly the bottleneck
in the case of large language models, the wire is the communication of your parameters between your layers of memory that is often the bottleneck. To do a forward pass, you need to use all parameters once, and so the communication between the compute and the storage is the bottleneck, and that bottleneck is also a bunch of wires.
> If you’re just using a code book to reconstruct a f16 model the only savings you can get are in sending it over the wire.
That’s why you need to use efficient gemm kernels like FLUTE for inference. They are ~as good as what you can do with ternary quantization.
If you want sub-2 bit llm, get one that’s already trained in higher precision, and compress it with something like YAQA/QTIP with finetuning or PV-tuning + AQLM/HIGGS
Only a presence bitmap? If we're contemplating packing schemes I'm tempted to write a paper that uses arithmetic coding to squeeze out a few more centi-bits.
Agreed. One possible objection might be that they need fast random access to weights, but I skimmed parts of the paper and it looks like they process 128 entries at a time, which to me sounds like it should be amenable to better compression: short enough that better compression results could still be efficiently cached in faster local RAM, long enough that better compression would save useful amounts of memory per block.
So this compression is only pertinent to the LLM file format? In memory it'd have to be expanded into the 1.58-bit form - 5 trits per byte.
It also means you can read them faster, more parameters per second during an inference which tends to be memory bandwidth limited on most systems. Thus faster inferences
sounds like a perfect fit for ASIC-optimized models (where matrix ops could be supported directly in BITCOS format, potentially) & achieving record power efficiency for on-device inference.
And it looks like per [0], a model needs only ~30% more weights to be at comparable quality, if quantization-aware training is done...
0. https://arxiv.org/pdf/2402.17764 - The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits
Pushing past log2(3) for real. This could drastically shrink LLMs for embedded systems, making them truly portable.
ternary is totally losslessly compressed anyway.
Why not just use an 8-bit LUT to encode the 256 most common ternary vectors with 6 components. That means of the possible 729 possible such vectors, you can only represent 256 different ones. You have to do more aggressive rounding, but at least the scheme is very simple to decompress and stream.
I think the weights are iid distributed, so all 729 patterns will be roughly equally likely. That doesn't make this a bad idea though -- it just means there's no point trying to select the most common 256 to keep, since any 256 will be roughly as good.
Very interesting, I was just exploring this to hopefully fit one of the latest quantized models in 16GB of VRAM.
This is the only time "1.58 bit" phrase makes more sense than "1 trit"
Who knew that if you actually look at information entropy you can pack stuff better!
Woah. Good science.
Thank you for sharing this. I like to test out running LLM's on edge computing with limited RAM and GPU/CPU so this research will have practical implications on my activities. I also appreciated how the authors formulated 1.58 (it's log_2(3)) because that was embarrassingly confusing for me when I was first introduced to ternary LLM's.
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