# NT@UW-22-03
Color Transparency and Light Front Holographic QCD

Gerald A. Miller<EMAIL_ADDRESS>Department of Physics, University of
Washington, Seattle, WA 98195, USA

###### Abstract

Color transparency, the reduction of initial- or final-state interactions in
coherent nuclear processes, is a natural prediction of QCD provided that
small-sized or point-like configurations (PLCs) are responsible for high-
momentum transfer, high-energy, semi-exclusive processes. I use the FMS
criteria for the existence of PLCs to show that the wave functions of light
front holographic QCD, as currently formulated, do not contain a PLC.

Color transparency is the amazing prediction of QCD that initial- and final-
state interactions are reduced in high-momentum transfer, high-energy coherent
reactions Frankfurt  _et al._ (1994); Jain  _et al._ (1996); Ashery (2006);
Dutta  _et al._ (2013). Strong interactions are strong: when hadrons hit
nuclei they generally break up the nucleus or themselves. Indeed, a well-known
semi-classical formula states that the intensity of a beam of hadrons falls
exponentially with the penetration distance through nuclei. This effect is
known as absorption. It is remarkable that QCD indicates that, under certain
specific conditions, the strong interactions can effectively be turned off and
hadronic systems can move freely through a nuclear medium.

This phenomenon is based on three requirements:

  * •

High momentum transfer coherent reactions are dominated by point-like color-
singlet components of the struck hadron wave function, denoted as PLCs. This
statement was a prediction intialy based on perturbative QCD (pQCD). For
example, early pQCD calculations Farrar and Jackson (1979); Efremov and
Radyushkin (1980); Lepage and Brodsky (1979a, b); Duncan and Mueller (1980a,
b, a), of the pion elastic electromagnetic form factor (see Fig. 1a) were
interpreted Mueller (1982) in the following manner: A high-momentum, $Q$,
photon hits one of the partons that greatly increases the relative momentum to
$Q$. The system can only stay together only by exchanging a gluon carrying
that momentum. That gluon has a range of only $1/Q$ so that the partons must
be close together, making a small-sized system or point-like configuration
(PLC). The validity of pQCD for computation of electromagnetic form factors is
a sufficient but not necessary condition for involvement of s PLC Frankfurt
_et al._ (1993) .

  * •

Small objects have small cross sections. It has been widely reported that the
imaginary part of the forward scattering amplitude, $f$ of a rapidly moving
color singlet object is proportional to the square of the transverse
separation, $b$, between positive and. negative color charges. The dominant
contribution to $f$, at high energies is given by two-gluon exchange Low
(1975); Nussinov (1975); Gunion and Soper (1977), and the remarkable feature
is that, in the limit that $b$ approaches 0, $f$ vanishes because color-
singlet point particles do not exchange colored gluons. This feature is
expressed concisely as $\lim_{b\to 0}\sigma(b^{2})\propto b^{2}.$ This reduced
interaction, caused by interference between emission by quarks of different
colors in coherent processes, is the basic ingredient behind QCD factorization
proofs, is widely used Donnachie  _et al._ (2004) and not questioned.

  * •

A PLC, once created, will expand as it moves. This is because a PLC is not an
eigenstate of the Hamiltonian. The expansion effect is diminished if the PLC
moves with sufficiently high momentum.

If all three requirements are satisfied for a given coherent process the
effects of color transparency will be evident.

The second and third items are based on many calculations, many experiments
and basic principles of quantum mechanics. The interesting dynamical question
is the validity or lack thereof of the idea the PLCs are involved. This
question is intimately connected with the origin of hadronic electromagnetic
form mechanism at high momentum transfer. In the perturbative QCD mechanism,
the large momentum transfer is taken up by the exchange of high-momentum
gluons. For this to occur, all of the partons must be at the same transverse
spatial location. Although it is natural to suppose that PLCs dominate
coherent high-momentum transfer processes, it is far from obvious that this is
the case Duncan and Mueller (1980a, b, a); Feynman (1972). For example, the
momentum transfer can involve a single quark of high momentum. This is the
Feynman mechanism, see Fig. 1, (first stated by Drell & Yan Drell and Yan
(1970)). The spectator system is not required to shrink to a small size and
color transparency effects involving protons would not be expected to occur.
In this picture, a reasonably valid relation between elastic and deep
inelastic scattering is obtained. See also West (1970). A more recent example
of a process that favors the Feynman mechanism appears in Radyushkin (1998).
See also Burkardt and Miller (2006). Note that Feynman remarked, “if a system
is made of 3 particles, the large $Q^{2}$ behavior depends not on the
singularity when just two come together, but rather when all three are on top
of one another”. Furthermore, “such pictures are too simple and inadequate”.

Figure 1:  High momentum transfer reaction mechanisms. Top picture: a pQCD
mechanism. Other diagrams of the same order are not shown. Middle picture:
Initial state in the Feynman mechanism. Bottom picture: final state in the
Feynman mechanism. The final state has a good overlap with the turned around
version of the initial state.

Models of Generalized Parton Distributions (GPDS) Ji (2004) access both the
longitudinal and transverse structure of nucleons so that measurements thereof
can distinguish the different mechanisms. It has been said Diehl (2003) that
GPDs parameterize soft dynamics akin to the Feynman mechanism. Specific models
of GPDs, for example de Teramond  _et al._ (2018) also favor the Feynman
mechanism. More generally, a review of the history teaches us Belitsky and
Radyushkin (2005) that there are only two proposals for the mechanism
responsible for high momentum elastic reactions.

Frankfurt, Miller & Strikman (FMS) introduced Frankfurt  _et al._ (1993) a
criteria to determine whether or not a given model of a hadronic wave function
admits the existence of a PLC. They found that a PLC could arise from non-
perturbative effects as well as from perturbative QCD. The aim of this paper
is to use the FMS criteria to see if the relativistic light-front wave
functions obtained from light front holographic QCD (see the review Brodsky
_et al._ (2015)) admit the existence of a PLC.

The first step is to discuss the FMS criterion. The idea is that a PLC is
originated via a hard probing interaction $T_{H}$ involving nucleons initially
bound in a nucleus. The soft interactions between the PLC and the surrounding
medium are proportional to the square of the transverse separation distance
Low (1975); Nussinov (1975); Gunion and Soper (1977) between constituents,
$b^{2}=\sum_{i<j}(b_{i}-b_{j})^{2},$ where the constituents are labelled
$i,j\cdots$ in first-quantized notation. Consider a high-momentum transfer
process on a nucleon. Denote the initial nucleon state as $|\psi(p)\rangle$
and the final state as $|\psi(p+q)\rangle$. Then represent the high momentum
transfer operator as $T_{H}(q)|\psi\rangle$. With this notation the form
factor $F(Q^{2})$ is given by the matrix element

$\displaystyle F(Q^{2})=\langle\psi(p+q)|T_{H}(q)|\psi(p)\rangle.$ (1)

The key question is whether the state $T_{H}(q)|\psi(p)\rangle$ is a PLC that
does not interact with the medium. The interaction with the surrounding medium
is proportional to $b^{2}$, the square of the transverse separation between a
struck parton and the remainder of the system. The first-order term in the
interaction is proportional to the matrix element
$\langle\psi(p+q)|b^{2}T_{H}(q)|\psi(p)\rangle$. This term is small if the
operator $T_{H}$ produces a PLC. The relevant comparison is with the form
factor $F(Q^{2})$ that is the process amplitude in the absence of final state
interactions. Thus FMS defined the quantity $b^{2}(Q^{2})$ as

$\displaystyle
b^{2}(Q^{2})={\langle\psi(p+q)|b^{2}T_{H}(q)|\psi(p)\rangle\over\langle\psi(p+q)|T_{H}(q)|\psi(p)\rangle}\equiv{F_{b^{2}}(Q^{2})\over
F(Q^{2})}$ (2)

If $b^{2}(Q^{2})=b^{2}(0)$ final state interactions of normal magnitudes
occur. If $b^{2}(Q^{2})$ drops with increasing values of $Q^{2}$, then the
model wave function is said to admit the existence of a PLC.

Now turn to evaluating $b^{2}(Q^{2})$ for wave functions obtained from
holographic techniques used represent relativistic light front wave
functionst, as discussed in the review Brodsky  _et al._ (2015). I briefly
discuss that approach. Light-front quantization is a relativistic, frame-
independent approach to describing the constituent structure of hadrons. The
assumed simple structure of the light-front (LF) vacuum allows a definition of
the partonic content of a hadron in QCD and of hadronic light-front theory
Brodsky  _et al._ (1998). The spectrum and light-front wave functions of
relativistic bound states are obtained in principle from the eigenvalue
equation $H_{LF}|\psi\rangle=M^{2}|\psi\rangle$ that becomes an infinite set
of coupled integral equations for the LF components. This provides a quantum-
mechanical probabilistic interpretation of the structure of hadronic states in
terms of their constituents at the same light-front time $x^{+}=x^{0}+x^{3}$,
the time marked by the front of a light wave Dirac (1949). The matrix
diagonalization Brodsky  _et al._ (1998) of the frame-independent LF
Hamiltonian eigenvalue equation in four-dimensional space-time has not been
achieved, so other methods and approximations Brodsky  _et al._ (2015) are
needed to understand the nature of relativistic bound states in the strong-
coupling regime of QCD.

To a first semiclassical approximation, where quantum loops and quark masses
are not included, the relativistic bound-state equation for light hadrons can
be reduced to an effective LF Schrödinger equation. The technique is to
identify the invariant mass of the constituents as a key dynamical variable,
$\zeta$, which measures the separation of the partons within the hadron at
equal light-front time de Teramond and Brodsky (2009). Thus, the multi-parton
problem in QCD is reduced, in a first semi-classical approximation, to an
effective one dimensional quantum field theory by properly identifying the key
dynamical variable. In this approach the complexities of the strong
interaction dynamics are hidden in an effective potential.

It is remarkable that in the semiclassical approximation described above, the
light-front Hamiltonian has a structure which matches exactly the eigenvalue
equations in AdS space Brodsky  _et al._ (2015). This offers the possibility
to explicitly connect the AdS wave function $\Phi(z)$ to the internal
constituent structure of hadrons. In fact, one can obtain the AdS wave
equations by starting from the semiclassical approximation to light-front QCD
in physical space-time. This connection yields a relation between the
coordinate $z$ of AdS space with the impact LF variable $\zeta$ de Teramond
and Brodsky (2009), thus giving the holographic variable $z$ a precise
definition and intuitive meaning in light-front QCD.

Light-front holographic methods were originally introduced Brodsky and de
Teramond (2006, 2008a) by matching the electromagnetic current matrix elements
in AdS space Polchinski and Strassler (2003) with the corresponding expression
derived from light-front quantization in physical space-time Drell and Yan
(1970); West (1970). It was also shown that one obtains identical holographic
mapping using the matrix elements of the energy-momentum tensor Brodsky and de
Teramond (2008b) by perturbing the AdS metric around its static solution
Abidin and Carlson (2008), thus establishing a precise relation between wave
functions in AdS space and the light-front wave functions describing the
internal structure of hadrons.

The light front wave functions that arise out of this light front holographic
approach provide a new way to study old problems that require the use of
relativistic-confining quark models. The study of the existence of a PLC by
evaluating $b^{2}(Q^{2})$ is an excellent example of such a problem.

I evaluate two examples. The first Brodsky and de Teramond (2008a) is an early
representation of the pion wave function as a $q\bar{q}$ system.

$\displaystyle\psi(x,b)={\kappa\over\sqrt{\pi}}\sqrt{x(1-x)}e^{-b^{2}\kappa^{2}x(1-x)/2}.$
(3)

I use the normalization $1=\int dxd^{2}b|\psi(x,b)|^{2}$ throughout this
paper. The wave function of Eq. (3) appears in many models. The form factor is
given by

$\displaystyle F(Q^{2})=\int dxd^{2}be^{i{\bf Q}\cdot{\bf
b}(1-x)}|\psi(x,b)|^{2},$ (4)

and evaluation yields

$\displaystyle F(Q^{2})=1-e^{Q^{2}/4\kappa^{2}}\Gamma(0,Q^{2}/4\kappa^{2}),$
(5)

with $\Gamma$ being the incomplete Gamma function. This form factor falls
asymptotically as $\sim 1/Q^{2}$, providing a nice example of how a non-
perturbative wave function can yield a power-law falloff. The limit for
$Q^{2}\to 0$ is also interesting:

$\displaystyle\lim_{Q^{2}\to
0}F(Q^{2})=1+(\gamma_{E}+\log(Q^{2}/4\kappa^{2}))Q^{2}/4\kappa^{2}+\cdots$ (6)

because of the appearance of the $\log$.

The quantity $F_{b^{2}}(Q^{2})$ is obtained by inserting a factor $b^{2}$ into
the integrand:

$\displaystyle F_{b^{2}}(Q^{2})=\int dxd^{2}b\,b^{2}\,e^{i{\bf Q}\cdot{\bf
b}(1-x)}|\psi(x,b)|^{2}$
$\displaystyle=-\nabla_{Q}^{2}\int{dx\over(1-x)^{2}}d^{2}be^{i{\bf Q}\cdot{\bf
b}(1-x)}|\psi(x,b)|^{2}$ (7)

Observe that $F_{b^{2}}$ is not simply obtained by differentiating the form
factor with respect to $Q^{2}$. This is because of the factor $1-x$ that
appears in the exponential function. Evaluation of the integral over the
transverse coordinates yields

$\displaystyle F_{b^{2}}(Q^{2})={1\over\kappa^{2}}\int{dx\,e^{-{Q^{2}\over
4\kappa^{2}}}\over x^{2}(1-x)}(x+{Q^{2}\over 4\kappa^{2}}(1-x)).$ (8)

The value of $F_{b^{2}}(Q^{2})$ is infinite for all values of $Q^{2}$ because
of the divergence (related to the $\log Q^{2}$ term in the form factor) as $x$
approaches unity. This shows that the simple wave function of Brodsky and de
Teramond (2008a) is not suitable for use in evaluating high energy forward
cross sections for pion-nucleus interactions.

The model given in Eq. (3) is very simple, so the next step is to use the
universal light front wave functions of Ref. de Teramond  _et al._ (2018).
This work presented a universal description of generalized parton
distributions obtained from Light-Front Holographic QCD, and I use their
models for light-front wave functions, presented as functions of the number
$\tau$ of constituents of a Fock space component. Regge behavior at small $x$
and inclusive counting rules as $x\rightarrow 1$ are incorporated. Nucleon and
pion valence quark distribution functions are obtained in precise agreement
with global fits. The model is described by the quark distribution
$q_{\tau}(x)$ and the profile function $f(x)$ with

$\displaystyle
q_{\tau}(x)=\frac{1}{N_{\tau}}\big{(}1-w(x)\big{)}^{\tau-2}\,w(x)^{-{\frac{1}{2}}}\,w^{\prime}(x),$
(9) $\displaystyle
f(x)=\frac{1}{4\lambda}\left[(1-x)\log\left(\frac{1}{x}\right)+a(1-x)^{2}\right],$
(10)

and $w(x)=x^{1-x}e^{-a(1-x)^{2}}.$

The value of the universal scale $\lambda$ is fixed from the $\rho$ mass:
$\sqrt{\lambda}=\kappa=m_{\rho}/\sqrt{2}=0.548$ GeV Brodsky  _et al._ (2015,
2016). The flavor-independent parameter $a=0.531\pm 0.037$. The $u$ and $d$
quark distributions of the proton are given by a linear superposition of
$q_{3}$ and $q_{4}$ while those of the pion are obtained from $q_{2}$ and
$q_{4}$. Ref. de Teramond  _et al._ (2018) also presents the universal light
front wave function:

$\displaystyle\psi_{\rm
eff}^{(\tau)}(x,\mathbf{b})=\frac{1}{2\sqrt{\pi}}\sqrt{\frac{q_{\tau}(x)}{f(x)}}(1-x)e^{-\frac{(1-x)^{2}}{8f(x)}\,\mathbf{b}^{2}},$
(11)

in the transverse impact space representation. The transverse coordinate $b$
again represents the relative distance between a struck parton and the
spectator system.

The form factor for a given value of $\tau$ is given by

$\displaystyle F^{(\tau)}(Q^{2})=\int dxq_{\tau}(x)e^{-Q^{2}f(x)},$ (12)

and $F^{(\tau)}_{b^{2}}{Q^{2}}$, obtained by inserting a factor $b^{2}$ into
the above integrand, is given by:

$\displaystyle F^{(\tau)}_{b^{2}}{Q^{2}}=\int dx{q_{\tau}(x)\over
4f(x)}e^{-Q^{2}f(x)}(1-{Q^{2}\over 16f(x)}(1-x)^{2}).$

Consider first the case of $\tau=2$. The use of Eq. (9) and Eq. (10) shows
that

$\displaystyle\lim_{x\to 1}{q_{2}(x)\over f(x)}={4\lambda\over(1-x)}+\cdots.$
(14)

Thus the same divergence that haunted the wave function of Eq. (3) reappears
for the more sophisticated $\tau=2$ wave function of de Teramond  _et al._
(2018) The functions
$b^{2}_{\tau}(Q^{2})=F^{(\tau)}_{b^{2}}{Q^{2}}/F^{(\tau)}{Q^{2}}$ for
$\tau=3,4$ are shown in Fig. 2.

Figure 2: $b^{2}_{\tau}(Q^{2})$ in units of GeV-2. The numbers refer to the
value of $\tau$, the number of constituents in the Fock state.

Observe that $b^{2}_{\tau}(Q^{2})$ rises with increasing values of $Q^{2}$, so
that these wave functions do not admit the existence of PLCs. Furthermore,
observe the surprising effect that constituents with larger number of partons
have smaller values of $b^{2}(Q^{2})$ and so interact less strongly with a
surrounding medium.

The summary of this work is that light front holographic wave functions do not
contain a PLC, so they do not predict the appearance of color transparency no
matter how large the value of $Q^{2}$. Adding a perturbative QCD tail to the
momentum-space wave function could change this result. The wave functions of
light front holographic QCD are suitable for describing the soft dynamics
involved the time evolution of a wave packet and were used Caplow-Munro and
Miller (2021) to interpret the recent striking experimental finding Bhetuwal
_et al._ (2021), that color transparency does not occur in $(e,e^{\prime}p)$
reactions with $Q^{2}$, up to 14.2 GeV2. The result is that the Feynman
mechanism is responsible for the proton form factor at high momentum transfer.

## Acknowledgements

This work was supported by the U. S. Department of Energy Office of Science,
Office of Nuclear Physics under Award Number DE-FG02-97ER- 41014. I thank the
organizers R. Dupre, D. Dutta, M. Sargsian and M. Strikman of the 2021
workshop on “The Future of Color Transparency and Hadronization Studies at
Jefferson Lab and Beyond” for re-stimulating my interest in this subject. I
thank S. J. Brodsky for making this paper necessary.

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# Efficient LLM Inference on CPUs

Haihao Shen Hanwen Chang Bo Dong Yu Luo Hengyu Meng
{haihao.shen, hanwen.chang, bo1.dong, yu.luo<EMAIL_ADDRESS>
###### Abstract

Large language models (LLMs) have demonstrated remarkable performance and
tremendous potential across a wide range of tasks. However, deploying these
models has been challenging due to the astronomical amount of model
parameters, which requires a demand for large memory capacity and high memory
bandwidth. In this paper, we propose an effective approach that can make the
deployment of LLMs more efficiently. We support an automatic INT4 weight-only
quantization flow and design a special LLM runtime with highly-optimized
kernels to accelerate the LLM inference on CPUs. We demonstrate the general
applicability of our approach on popular LLMs including Llama2, Llama, GPT-
NeoX, and showcase the extreme inference efficiency on CPUs. The code is
publicly available at: https://github.com/intel/intel-extension-for-
transformers.

##  1 Introduction

Large language models (LLMs) have shown remarkable performance and tremendous
potential across a wide range of tasks Rozière et al. (2023); Touvron et al.
(2023b, a); Zhang et al. (2022); Brown et al. (2020); Li et al. (2023).
However, deploying these models has been challenging due to the astronomical
amount of model parameters, which necessitates significant memory capacity and
high memory bandwidth.

Quantization is a technique to reduce the numeric precision of weights and
activations of a neural network to lower the computation costs of inference.
INT8 quantization Vanhoucke et al. (2011); Han et al. (2015); Jacob et al.
(2018) is the most widely-used approach today given the trade-off between high
inference performance and reasonable model accuracy. However, outliers in
activations have been observed and those outlier values are limiting the
general adoption of INT8 quantization, though there are some related work that
has been proposed to address the issues Xiao et al. (2023); Wei et al. (2023);
Dettmers et al. (2022). FP8 is a newly introduced data type that has attracted
lots of attentions Micikevicius et al. (2022); Kuzmin et al. (2022); Sun et
al. (2019); Shen et al. (2023) while it has little adoptions due to the
hardware unavailability. On the other hand, weight-only quantization becomes
popular as it applies the low precision (e.g., 4-bit) to weights only, while
keeping higher precision (e.g., 16-bit floating point) for activations,
therefore maintaining the model accuracy. There are many excellent work on
4-bit weight-only quantization Dettmers et al. (2023); Frantar et al. (2022);
Cheng et al. (2023b); Lin et al. (2023); Kim et al. (2023); Wu et al. (2023);
Cheng et al. (2023a) that have demonstrated the effectiveness in LLM
inference. Meanwhile, the open-source community is embracing such low-bit
weight-only quantization and offers the CPP-based implementations such as
llama.cpp and starcoder.cpp based on ggml library. These implementations are
typically optimized for CUDA and may not work on CPUs. Therefore, it is
important to address the challenge of making LLM inference efficient on CPU.

In this paper, we propose an effective approach for LLM inference on CPUs
including an automatic INT4 quantization flow and an efficient LLM runtime. We
leverage Intel Neural Compressor that provides the support of INT4
quantization such as GPTQ Frantar et al. (2022), AWQ Lin et al. (2023), TEQ
Cheng et al. (2023a), SignRound Cheng et al. (2023b) and generate the INT4
model automatically. Inspired from the ggml library, we develop a tensor
library for CPU, supporting all the mainstream instruction sets such as AVX2,
AVX512, AVX512_VNNI Rodriguez et al. (2018), and AMX (Advanced Matrix
Extensions). Our results show the average latency of generation tokens from
20ms to 80ms on LLMs with 6B to 20B parameters using just a single socket of
4th Generation Intel® Xeon® Scalable Processors, while preserving the high
accuracy within only 1% loss from FP32 baseline. Our main contributions are as
follows:

  * •

We propose an automatic INT4 quantization flow and generate the high-quality
INT4 models with negligible accuracy loss within <1% from FP32 baseline.

  * •

We design a tensor library that supports general CPU instruction sets and
latest instruction sets for deep learning acceleration. With CPU tensor
library, we develop an efficient LLM runtime to accelerate the inference.

  * •

We apply our inference solution to popular LLM models covering 3B to 20B and
demonstrate the promising per-token generation latency from 20ms to 80ms, much
faster than the average human reading speed about 200ms per token.

The rest of this paper is organized as follows. Section 2 introduces the
approach including INT4 quantization and inference. Section 3 outlines the
experimental setup, presents accuracy & performance results, and offers
discussion on performance tuning. Section 4 presents the conclusions and
future work.

##  2 Approach

In this section, we introduce the approach which consists of two major
components: an automatic INT4 quantization flow and an efficient LLM runtime,
as shown in Figure 1. More details are described in the following sections.

Figure 1: The left part is the automatic INT4 quantization flow: given a FP32
model, the flow takes the default INT4 quantization recipes and evaluates the
accuracy of INT4 model; the recipe tuning loop is optional, if INT4 model can
meet the accuracy target. The right part is a simplified runtime for efficient
LLM inference built on top of a CPU tensor library with automatic kernel
selector.

###  2.1 Automatic INT4 Quantization Flow

INT4 quantization flow is developed based on Intel Neural Compressor, a
popular quantization tool for deep learning frameworks. Since the tool has
already supported the mainstream INT4 quantization recipes such as GPTQ,
SignRound, AWQ, TEQ, and RTN (round-to-nearest), our automatic quantization
flow allows the recipe tuning on different quantization recipes, different
granularities (channel-wise or group-wise), different group size (32, 64, 128
… 1024). Each recipe generates an INT4 model that is evaluated in the flow.
Once the INT4 model meets the accuracy target, the model will be passed to LLM
Runtime for performance evaluation.

###  2.2 Efficient LLM Runtime

LLM runtime is designed to provide the efficient inference of LLMs on CPUs.
Figure 2 describes the key components in LLM runtime, where the components
(CPU tensor library and LLM optimizations) in green are specialized for LLM
inference, while the other components (memory management, thread scheduler,
operator optimization and fusion) in blue are required for a general runtime.
More details about CPU tensor library and LLM optimizations are described in
the following paragraphs, while the general components are omitted due to the
space limitations. Note that the design is flexibly extensible with hardware
abstraction layer (CPU only for now), while how to support other hardware is
out of scope in this paper.

Figure 2: Key components in LLM runtime: general and LLM specialized.

#### CPU Tensor Library.

We develop CPU tensor library for linear algebra subroutines, inspired from
the template design of cutlass. The tensor library offers a comprehensive
support of INT4 kernels for x86 CPUs as shown in Table 1, where AMX is
available in the latest Intel Xeon Scalable Processors and VNNI is available
in both Intel and AMD CPUs.

Table 1: Support matrix by CPU tensor library: input/output data type, compute data type, and ISA (instruction set architecture). The library supports dynamic quantization for input along with batch or input channel per group, and weight quantization in both symmetric and asymmetric scheme. Input Data Type | Output Data Type | Compute Data Type | Compute ISA
---|---|---|---
FP32 | FP32 | FP32 | AVX2
FP32 | FP32 | FP32 | AVX512F
FP32 | FP32 | INT8 | AVX_VNNI
FP32 | FP32 | INT8 | AVX512_VNNI
FP32 | FP32 | INT8 | AMX_INT8
FP32/FP16 | FP32/FP16 | FP16 | AVX512_FP16
FP32/BF16 | FP32/BF16 | BF16 | AMX_BF16

#### LLM Optimizations.

Most recent LLMs are typically decoder-only Transformer-based models Vaswani
et al. (2017). Given the unique characteristics of next token generation, KV
cache becomes performance critical for LLM inference. We describe the
optimizations in Figure 3.

(a)

(b)

Figure 3: KV cache optimization. Left (a) shows the default KV cache, where
new token generation requires memory reallocation for all the tokens (5 in
this example); right (b) shows the optimized KV cache with pre-allocated KV
memory and only new token updated each time.

##  3 Results

###  3.1 Experimental Setup

To demonstrate the generality, we select the popular LLMs across a wide range
of architectures with the model parameter size from 7B to 20B. We evaluate the
accuracy of both FP32 and INT4 models using open-source datasets from lm-
evaluation-harness including lambada Paperno et al. (2016) openai, hellaswag
Zellers et al. (2019), winogrande Sakaguchi et al. (2021), piqa Bisk et al.
(2020), and wikitext. To demonstrate the performance, we measure the latency
of next token generation on the 4th Generation Intel® Xeon® Scalable
Processors, available on the public clouds such as AWS.

###  3.2 Accuracy

We evaluate the accuracy on the aforementioned datasets and show the average
accuracy in Table 2. We can see from the table that the accuracy of INT4 model
is nearly on par with that of FP32 model within 1% relative loss from FP32
baseline.

Table 2: INT4 and FP32 model accuracy. INT4 model has two configurations: group size=4 and 128. LLM | FP32 | INT4 (Group size=32) | INT4 (Group size=128)
---|---|---|---
EleutherAI/gpt-j-6B | 0.643 | 0.644 | 0.64
meta-llama/Llama-2-7b-hf | 0.69 | 0.69 | 0.685
decapoda-research/llama-7b-hf | 0.689 | 0.682 | 0.68
EleutherAI/gpt-neox-20b | 0.674 | 0.672 | 0.669
tiiuae/falcon-7b | 0.698 | 0.694 | 0.693

###  3.3 Performance

We measure the latency of next token generation using LLM runtime and the
popular open-source ggml-based implementation. Table 3 presents the latency
under a proxy configuration with 32 as both input and output tokens. Note that
ggml-based solution only supports group size 32 when testing.

Table 3: INT4 performance using LLM runtime and ggml-based solution. LLM runtime outperforms ggml-based solution by up to 1.6x under group-size=128 and 1.3x under group size=32. model |  | LLM Runtime
---
(Group size=32)
| LLM Runtime
---
(Group size=128)
| ggml-based
---
(Group size=32)
EleutherAI/gpt-j-6B | 22.99ms | 19.98ms | 31.62ms
meta-llama/Llama-2-7b-hf | 23.4ms | 21.96ms | 27.71ms
decapoda-research/llama-7b-hf | 23.88ms | 22.04ms | 27.2ms
EleutherAI/gpt-neox-20b | 80.16ms | 61.21ms | 92.36ms
tiiuae/falcon-7b | 31.23ms | 22.26ms | 36.22ms

###  3.4 Discussion

Though we demonstrate the performance advantage over ggml-based solution,
there are still opportunities for LLM runtime to further improve the
performance through additional performance tuning such as thread scheduler in
LLM runtime, blocking strategy in CPU tensor library.

##  4 Summary and Future Work

We presented an end-to-end INT4 LLM inference including an automatic INT4
model quantization and efficient LLM runtime. We demonstrated the generality
on a set of popular LLMs and the performance advantage over the open-source
solution on CPUs. As our future works, we plan to further improve the CPU
tensor library and extend Hugging Face transformer APIs to support INT4 LLM
inference as part of the contributions to the open-source community. Moreover,
we plan to exercise our approach on personal computers (PCs) given the broad
accessibility of CPUs, to meet the growing demands of AI generated content and
empower generative AI on PCs.

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