# A Precision-Optimized Fixed-Point Near-Memory Digital Processing Unit for
Analog In-Memory Computing

Elena Ferro132, Athanasios Vasilopoulos2, Corey Lammie2, Manuel Le Gallo2,
Luca Benini3, Irem Boybat12, Abu Sebastian2
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0000-0002-8618-8643 0009-0001-9081-6139 0000-0001-5564-1356
0000-0003-1600-6151 0000-0001-8068-3806 0000-0002-4255-8622
0000-0001-5603-5243 2 IBM Research Europe, 8803 Rüschlikon, Switzerland,3 IIS-
ETH Zürich, 8092 Zürich, Switzerland
1Email: {elf<EMAIL_ADDRESS>
###### Abstract

Analog In-Memory Computing (AIMC) is an emerging technology for fast and
energy-efficient Deep Learning (DL) inference. However, a certain amount of
digital post-processing is required to deal with circuit mismatches and non-
idealities associated with the memory devices. Efficient near-memory digital
logic is critical to retain the high area/energy efficiency and low latency of
AIMC. Existing systems adopt Floating Point 16 (FP16) arithmetic with limited
parallelization capability and high latency. To overcome these limitations, we
propose a Near-Memory digital Processing Unit (NMPU) based on fixed-point
arithmetic. It achieves competitive accuracy and higher computing throughput
than previous approaches while minimizing the area overhead. Moreover, the
NMPU supports standard DL activation steps, such as ReLU and Batch
Normalization. We perform a physical implementation of the NMPU design in a 14
nm CMOS technology and provide detailed performance, power, and area
assessments. We validate the efficacy of the NMPU by using data from an AIMC
chip and demonstrate that a simulated AIMC system with the proposed NMPU
outperforms existing FP16-based implementations, providing 139 $\times$ speed-
up, 7.8 $\times$ smaller area, and a competitive power consumption.
Additionally, our approach achieves an inference accuracy of 86.65 %/65.06 %,
with an accuracy drop of just 0.12 %/0.4 % compared to the FP16 baseline when
benchmarked with ResNet9/ResNet32 networks trained on the CIFAR10/CIFAR100
datasets, respectively.

###### Index Terms:

Near-memory processing, Fixed-point computing, Analog in-memory computing,
Deep learning, AI

##  I Introduction

The recent growth in the Artificial Intelligence (AI) domain has been driven
by the shift from compute-centric systems to data-centric computing systems
[1]. However, conventional von Neumann architectures exploiting data-level
parallelism are bound by the _memory-wall_ , as well as the microarchitectural
challenges imposed by the increasing degree of concurrency required, which
affect latency and energy efficiency [2, 3, 4]. To overcome these limitations,
a promising alternative leverages non-von Neumann architectures, which perform
computational tasks within the memory itself. This paradigm, known as In-
Memory Computing (IMC), tackles the von Neumann bottleneck, leading to
significant improvements in both energy efficiency and latency. A promising
realization of IMC is Analog In-Memory Computing (AIMC), with recent works
showcasing its potential [5, 6, 7]. The Matrix-Vector-Multiplication (MVM)
operation, which dominates the computations ($>$95 %) of Deep Neural Network
(DNN) inference, can be performed by mapping offline-trained network weights
onto AIMC tiles. Consequently, AIMC is a very promising approach for
accelerating these workloads [8]. For example, a single 256$\times$256 Phase
Change Memory (PCM) tile has been shown to achieve a peak energy efficiency of
$\sim$10 TOPS/W [5, 6] while innovative design approaches are aiming for
$\sim$100 TOPS/W [9].

Figure 1: (a) Sample AIMC tile consisting of a 256$\times$256 PCM crossbar,
DAC block, 256 ADCs and 64 NMPUs; (b) flow diagram of the proposed fixed-point
NMPU.

A typical AIMC-tile comprises a crossbar array of memristive devices, such as
PCM. The synaptic weights are programmed as the conductance value of these
devices. The digital input to the tile is converted to voltage or pulse
duration values using Digital-to-Analog Converters (DACs) or pulse-width
modulation units, respectively, and the output from the array is converted to
digital values using Analog-to-Digital Converters (ADCs). However, one key
challenge is that there is substantial non-uniformity in the ADCs’ conversion
behavior (or transfer curves). To address this, AIMC tiles require additional
data post-processing per column through an _affine correction_ procedure
computed as:

$d_{\text{out},\text{aff}}=d_{\text{in}}\times\text{scale}_{\text{aff}}+\text{offset}_{\text{aff}},$
(1)

where $d_{\text{in}}$ is the output of the ADC, and
$\text{scale}_{\text{aff}}$ and $\text{offset}_{\text{aff}}$ are the affine
correction parameters. These parameters can also be leveraged to perform any
subsequent scaling and offset operation on $d_{\text{out},\text{aff}}$. For
instance, PCM devices exhibit significant temporal conductance drift and the
conductance values also vary with temperature. These effects can be partially
compensated by using correction factors [10, 11]. Moreover, the affine
correction parameters can also realize Batch Normalization (BN) when
implementing DNNs such as Convolutional Neural Networks (CNNs). Hence, by
providing additional support for the Rectified Linear Unit (ReLU) activation
function, the AIMC tile periphery provides compatibility with CNN auxiliary
operations. Therefore, we formulate the operations to be performed by near-
memory processing block targeting CNN implementations as follows:

$d_{\text{out}}=\text{ReLU}(d_{\text{in}}\times\text{scale}+\text{offset}).$
(2)

Clearly, near-memory digital processing is an indispensable part of an AIMC
tile. To achieve high computational efficiency and low latency in AIMC
systems, it is desirable to integrate the custom near-memory digital logic
circuitry for each crossbar column. However, maximizing the area efficiency of
the tile (TOPS/mm2), as well as complying with the small pitch of the AIMC
columns and the ADCs (for instance, 4 $\mu$m in [5]), heavily constraints the
available area budget and the physical implementation of this block (Fig. 1a).
Therefore, a flexible solution maintaining high energy efficiency and accuracy
while being compact and fast is required. Designs using Floating Point 16
(FP16) datatypes were explored in prior works [5, 6]. However, these
approaches incur a relatively large area and power consumption. This leads to
a large digital block shared across multiple columns (e.g., 256 columns in
[6]), which limits parallelization and requires serial pipelined processing
for all outputs. An alternative is the adoption of standard integer types,
which reduce the area overhead and enable multiplexing across 8 [12] or 16
[13] crossbar columns.

In this paper, we address the limitations of existing solutions by proposing a
flexible Near-Memory digital Processing Unit (NMPU) that leverages fixed-point
precision computation to perform accurate affine correction and auxiliary
operations while minimizing its area footprint. Our design can be multiplexed
across just 4 memristive crossbar array columns and, compared to [12, 13],
adopts truncation and rounding schemes, significantly reducing the size of
intermediate representations for a more compact design. We experimentally
validate the effectiveness of our approach using ADC data from a PCM-based
AIMC chip [5].

##  II NMPU microarchitecture and design space exploration

The NMPU microarchitecture implementing the computations of (2) is shown in
Fig. 1b. The design consists of two identical branches, which apply different
scale parameters to the digitized values of positive and negative currents
coming from one ADC as distinct paths [5, 6]. The block consumes two 10-bit
unsigned integer inputs and produces an 8-bit signed output. In addition, the
unit implements rounding and truncation steps to reduce intermediate precision
and mitigate precision loss during the computations. The design is fully
parameterizable in terms of the inputs, scale, shift and offset factors,
intermediate truncation formats, and output format. In the following, we
explore optimal parameters for the proposed block. For this analysis, we set
the input and output formats as 10-bit unsigned (integer) and 8-bit signed
(2’s complement), respectively. The choice of the input format is based on the
adoption of a 10-bit ADCs’ design, while 8-bit outputs for activations are
widely adopted for Deep Learning (DL) inference acceleration [14, 4, 15, 16,
17].

First, we determine the optimal data formats for scale and offset constants by
analyzing the ADC transfer curves, which are experimentally acquired from
circuit measurements of [5] and shown in Fig. 2.

Figure 2: Set of 256 ADC transfer curves: after calibration in purple; and
after the affine correction in orange.

They are obtained for a set of 256 distinct ADCs after being properly
calibrated [5]. The individual trajectories highlight the variations across
individual ADCs, and the relationship between the bit-line current and the
converted ADC counts is observed to be nonlinear. The affine correction (see
(1)) minimizes the variation of the curves with respect to their mean, i.e.,
tuning the slope with a certain precision granularity. We estimate the maximum
and minimum scaling factors for the affine correction as 0.88 and 1.17,
respectively. Hence, 1-bit for the integer part is sufficient in the
corresponding fixed-point number. On the other hand, the fractional part
depends on the desired precision for the tuning, which is targeted to be
higher than the precision of the Coefficient of Variation (CV) in the set of
256 ADCs transfer curves. Since the CV is observed to be $\simeq$7 % of the
mean, we retain a granularity of 1 %, which corresponds to $\simeq 2^{-7}$,
i.e., 7-bit. Thus, we need 1-bit and 7-bit to represent the integer and
fractional part of the scale parameter, respectively, i.e., (1,7) bit
unsigned. For the offset parameter, we observe that (4,0) bit signed is
sufficient to account for the measured offset. However, we allocate more bits
to accommodate for any further requirement associated with the BN operation
and propose using (7,1) bit signed.

To perform the scaling in high precision and to ensure that the scaled values
fit the output range, we introduce a right shift operation after the scale
(see Fig. 1b). Given that the ADCs’ output precision is 10-bit unsigned, the
scale is 1-bit precision for the integer part, and the output is 8-bit signed,
the maximum value needed for the right shift is three, which can be
represented with 2 bits. In addition, since the shift operation ensures the
range fits 8-bit, we reduce the integer bits by cutting the unused Most
Significant Bits (MSBs), i.e., ($2^{2}-1$) MSBs. Furthermore, since a high
degree of precision is unnecessary when determining the methodology for
conducting the rounding operation, we truncate the Least Significant Bits
(LSBs) up to and including $2^{-6}$.

Figure 3: Quantization error for the 15 explored NMPUs adopting different
first and second cut/round stages.

To evaluate the influence of cut and round operations on the overall precision
loss, we consider 15 distinct architectures leveraging a different combination
of cut/round methods after the scaling (first cut/round stage) and the sum
(second cut/round stage). We denote as guard (G) and round (R) the bits that
determine whether a truncation or rounding should occur, respectively, and as
x the bits not affecting the decision. For the first cut/round stage, we
consider five methods: 1 cut 3 LSBs up to $2^{-2}$ (excluded) and round only
looking at the bit at position $2^{-3}$ (x.xx$|$Rxx); 2 cut 3 LSBs up to
$2^{-2}$ (excluded) and if the bit at position $2^{-2}$ is 1 then we cut;
otherwise, we round looking at the bits at position $2^{-3}$ or $2^{-4}$ (if
at least one is 1) (x.xG$|$RRx); 3 cut 3 LSBs up to $2^{-2}$ (excluded) and if
the bit at position $2^{-2}$ is 1 then we cut; otherwise, we round looking at
the bit at position $2^{-3}$ (x.xG$|$Rxx); 4 cut 3 LSBs up to $2^{-2}$
(excluded) and if the bit at position $2^{-2}$ is 1 then we cut; otherwise, we
round looking at the bit at position $2^{-3}$ or $2^{-4}$ or $2^{-5}$
(x.xG$|$RRR); 5 cut 3 LSBs up to $2^{-2}$ (excluded) (x.xx$|$xxx).

For each of these methods, we consider three ways of performing the second
cut/round stage: I cutting the LSB for both positive and negative values; II
rounding the LSB for positive and cutting LSB for negative values; and III
rounding LSB for both positive and negative values.

##  III Evaluating precision of the proposed datapath

To evaluate the impact of the two cut/round stages on the precision loss, we
evaluate the architectures with a cycle-accurate Register Transfer Level (RTL)
simulator, using randomly generated data from a univariate normal Gaussian
distribution with mean 0 and variance 1 for the inputs. As an evaluation
metric for the precision loss, we compute the quantization error against a
software-based (FP32) baseline:

$Q_{\text{err}}=|\text{out\\_hardware}-\text{out\\_baseline}|$ (3)

Figure 4: Relative quantization error on ResNet9 layers.

Being the output integer, the best architectures provide the lowest percentage
of data with $Q_{\text{err}}\geq 0.5$, as shown in Fig. 3. We observe that
$Q_{\text{err}}$ is mainly affected by the method adopted for the _second
cut/round stage_. In particular, the architectures implemented with I have
less than 11 % of data (over a range of 10,000 data points) with
$Q_{\text{err}}\geq 0.5$. We continue the analysis by selecting the two most
performant architectures (A and B), as well as the least performant for each
method in the second cut/round stage (C, D and E), as shown in Fig. 3.

Next, we implement Python models for the selected architectures and evaluate
them using ADC data from the chip presented in [5]. Data is extracted during
inference on a modified ResNet9 model [18]. We compare the relative
quantization error on a layer-by-layer basis (i.e., without any layer
propagation) with the software baseline. More specifically, the error per
layer is evaluated as follows. First, we compute the MVM and, where
applicable, the BN, all in FP32, to serve as a software baseline. Second, we
estimate the hardware operation error (“hw_op_err”) resulting from performing
both MVM and analog-to-digital conversion on chip when the affine correction
and BN are performed in FP32 (AIMC-baseline). This hardware operation error is
computed as the root-mean-squared (L2) error between the AIMC-baseline and the
software baseline results. Then, we estimate the L2-error between the software
baseline and the proposed implementations (referred to as “impl_err”), where
the MVM is performed on-chip and the affine correction and BN are performed
with the selected NMPU variants. Finally, the relative quantization error is
calculated as:

$Q_{\text{err\\_rel}}=\frac{\text{impl\\_err -
hw\\_op\\_err}}{\text{hw\\_op\\_err}}.$ (4)

Fig. 4 shows that the NMPU block incurs a relative quantization error $<$4 %
and $<$2 % compared to the AIMC-baseline and to the FP16-based post-processing
implementation from [5] for all layers, respectively. When including BN,
$Q_{\text{err\\_rel}}$ increases for both the NMPU and the FP16 compared to
the AIMC-baseline. In both situations, NMPU’s $Q_{\text{err\\_rel}}$ varies
with a trend similar to that of Fig. 3. In the best case, i.e., ArchA, the
NMPU achieves a $Q_{\text{err\\_rel}}<$1 % compared to FP16. Consequently, in
circuit applications, where the absolute value on the output is crucial,
exploring different cut/round methods is important to identifying the
architecture with the lowest output error. However, when targeting DL
applications, the final goal is the accuracy assessment rather than comparing
absolute output values. Therefore, in the following, we investigate the impact
of the quantization error on the accuracy evaluation, building towards a more
comprehensive application study.

Figure 5: Inference accuracy for ResNet9 and ResNet32 for different
architectures. The error bars represent the standard deviation obtained from
10 repetitions.

Besides the previous evaluation, we feed the output of the near-memory post-
processing block to the AIMC tile containing the weights of the subsequent
layer. For this study, we simulate the hardware using statistical models
extracted from chip measurements [6] and explore both ResNet9 and a deeper
ResNet32 [19] on the CIFAR10 and CIFAR100 datasets, respectively. Fig. 5 shows
the results obtained via simulations. We observe an accuracy degradation from
the software baseline (similar to that of Fig. 4) when the hardware model is
used. The hardware model employs statistical models of the chip to simulate
the MVM and data converters, while the affine correction and BN are performed
in FP32. In the other implementations from Fig. 5, the hardware model is
revised to perform the affine correction and BN using FP16 [5] or the proposed
NMPUs. For ResNet9 on the CIFAR10 dataset, the selected architectures show an
inference accuracy drop $\leq$ 2.1 % compared to the software baseline, $\leq$
0.7 % compared to the hardware model with an FP32 periphery, and $\leq$ 0.5 %
compared to the FP16 [5] model. Overall, independently of the observed
$Q_{\text{err}}$, the fixed-point-based NMPUs do not significantly affect the
inference accuracy, whose degradation is instead dominated by the MVM non-
idealities.

Since the accuracy of the explored architectures is similar, for ResNet32 on
the CIFAR100 dataset and for the following explorations, we consider only the
architecture with the highest inference accuracy mean, i.e. 86.648 %, referred
to as ArchA. Fig. 5 shows that, ArchA, achieves an inference accuracy of
86.648 %/65.061 % on the CIFAR10/CIFAR100 dataset, with an accuracy drop of
only 0.12 %/0.4 % compared to an FP16-based near-memory logic.

To enhance the consistency of our study, the NMPU based on ArchA has been
integrated into the software stack of the hardware platform proposed by [5],
enabling chip-in-the-loop simulation. The existing FP16-based near-memory
logic has been disabled from the physical chip. The chip is linked with the
software environment where the NMPU is implemented through a communication
infrastructure that allows them to interact for the computation of subsequent
layers. Fig. 5 shows the results for ResNet9 trained on CIFAR10 dataset when
using a real hardware platform (marked with a star in the figure). As the
previous simulations did not account for all chip non-idealities, the real-
hardware experiments show an accuracy degradation compared to software
simulations. Nonetheless, the proposed fixed-point NMPU implementation
achieves competitive performance compared to the FP16-based system, consistent
with the simulation results. To fully exploit the benefits of adopting a
flexible fixed-point-based architecture, in the next section, we detail its
physical implementation and power, performance and area (PPA) assessment.

##  IV Synthesis of NMPU in 14nm CMOS technology

We synthesize ArchA using Cadence Genus 20.11 and perform physical
implementation using Cadence Innovus 21.13 in a 14 nm CMOS technology. The
resulting PPA estimations are shown in Table I. The NMPU results in a 505
$\times$ area reduction compared to FP16 [5], whose area is estimated to be
about 1.67 MGE (Gate Equivalent). The significant area reduction enables to
time-multiplex the NMPU across 4 columns of architectures with an ADC pitch of
4 $\mu$m, e.g. [5, 6]. Therefore, the lean design allows fitting 64 NMPUs
operating in parallel in such systems. The resulting latency and power
consumption for post-processing of an AIMC core [5] read 4 ns and 24.5 mW,
respectively. This implies that the proposed approach is 139 $\times$ faster
than FP16 [5], which requires about 558 ns to process all the 256 outputs in a
serial-pipelined fashion. The micrograph of the unit, including two fixed-
point-based NMPUs, the configuration registers for the scale and offset
parameters, and the test interface is shown in Fig. 6.

TABLE I: Post-layout metrics in 14nm

System |  Area (kGE) |  Latency (ns) |  Tot Latency (ns) | Power (mW)
---|---|---|---|---
SS | FF
ArchA | 3.3 | 1 | 256 | 0.383 | 0.524
ArchA$\times$64 | 211 | 1 | 4 | 24.5 | 33.5
FP16 [5] | 1666 | 46 | 558 | 27 (post-layout=32)

Figure 6: Micrograph of the implemented block in 14nm.

##  V Conclusion

In this paper, we proposed a fixed-point NMPU designed, simulated, and
physically implemented using 14 nm CMOS technology. Our NMPU achieves
competitive precision on both small and large networks, i.e., ResNet9 and
ResNet32, with accuracy drops of only 0.12 % and 0.4 % compared to existing
AIMC solutions adopting FP16 precision while minimizing the area overhead by
505 $\times$. Furthermore, due to NMPU’s compact form factor, we proved its
high-parallelization capability by fitting $\times$64 fixed-point based NMPUs
in a 7.8 $\times$ smaller area than the FP16-based implementation of [5]. This
results in a 139 $\times$ speed-up for the whole post-processing computation
without increasing the power consumption.

##  VI Acknowledgments

We thank M. Ishii and M. Brändli for technical support. This work was
supported by IBM Research AI Hardware Center, European Union’s Horizon Europe
Research and Innovation Program (Grant 101070634), and Swiss State Secretariat
for Education, Research and Innovation (SERI) (Grant 23.00205).

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# GENERAL THEOREM ON INTERPOLATION OF COMPACT OPERATORS

Evgeniy Pustylnik

Technion, Haifa 32000, Israel
E-mail: evggmail.com

We prove an abstract theorem on keeping the compactness property of a linear
operator after interpolation in Banach spaces. No analytical presentation of
operators, spaces and interpolation functor is required. We use only some
little-known properties of compact sets and various facts about bases and
basic sequences (with detailed references to the monograph “Bases in Banach
spaces”, Vol. I–II by I.M.Singer). Therefore the results are applicable to
arbitrary spaces and any interpolation functor, including the complex method.
The “two-sided” compactness is also mentioned at the end of this paper as a
mere corollary.

Compact operators, interpolation, basic sequences

###### :

46B70

1. In this paper we show that the interpolation of “one-sided” compactness of arbitrary linear operators is possible for any Banach couples and every interpolation functor. We start our investigations with embedding operators, since the consequent pass to arbitrary operators was already considered by M. Cwikel, N. Krugljak and M. Mastyło in [1] (see Appendix at the end of this paper).

So, let $(A_{0},A_{1}),\,(B_{0},B_{1})$ be two nontrivial Banach couples with
an interpolation functor $\Cal{F}$, defined on them. Let $A_{0}\hookrightarrow
B_{0},\,A_{1}\hookrightarrow B_{1}$ and $J$ be the corresponding embedding
operator. Thus, due to interpolation, $J$ gives an embedding
$\Cal{F}(A_{0},A_{1})=A\hookrightarrow B=\Cal{F}(B_{0},B_{1})$. The problem is
to prove compactness of the last embedding if such is the embedding
$J:A_{1}\to B_{1}$ (one-sided compactness).

Of course, the one-sided compactness of embedding for an intermediate space
may be impossible if this space is not sufficiently distant from the second
space of the couple, where the compactness is not given. This imposes some
additional restrictions on the interpolation functor, which must contain an
implicit measure of admissible distance. For example, those restrictions are
shown as necessary for some cases of real interpolation in the papers [2], [3]
etc.

In our paper such a restriction will be used in the following form: there
exists a function $W(\alpha,\beta),\ \alpha,\beta>0$, with $\lim_{\beta\to
0}W(\alpha,\beta)=0$ when $\sup\alpha<\infty$, such that

$\|T\|_{A\to B}\leq W(\|T\|_{A_{0}\to B_{0}},\|T\|_{A_{1}\to B_{1}})$ $None$

for any linear operator $T:A_{0}+A_{1}\to B_{0}+B_{1}$. For example, in the
case of a complex interpolation functor $\Cal{F}_{[\theta]},\ 0<\theta<1$,
such a function exists in the form
$W(\alpha,\beta)=\alpha^{1-\theta}\beta^{\theta}$.

###### Main Theorem

Under conditions on the spaces $(A_{0},A_{1}),\,(B_{0},B_{1})$ and the functor
$\Cal{F}$ posed above, the embedding $A\hookrightarrow B$ is compact.

We shall use the following standard way of the proof. We suppose, on the
contrary, that the embedding $A\hookrightarrow B$ is not compact. Then there
exists a bounded infinitely dimensional sequence $(x_{n})\subset A,\ x_{n}\neq
0$, with no convergent subsequence in $B$. It follows immediately from this
that the sequence of the norms $\|x_{n}\|_{B}$ is bounded from below too,
namely, $\inf\|x_{n}\|_{B}>0$. This fact can be proved exactly as in Theorem
4.2 from [4] due to non-compactness of embedding $A\hookrightarrow B$, since
every unbounded from below set necessarily contains a sequence converging to
zero. The infinite dimension of the sequence $(x_{n})$ also follows from its
non-compactness in $B$, because each set with finite dimension is compact in
any topology.

Together with the embedding inequality between norms in spaces $A$ and $B$, we
obtain the following assertion.

###### Corollary

The assumption on non-compactness of embedding $A\hookrightarrow B$ implies
existence of an infinitely dimensional bounded from above and below sequence
$(x_{n})$ with equivalent norms $\|x_{n}\|_{A}$ and $\|x_{n}\|_{B}$.

Just one of such sequences will be the main object in our next discussions.

2. Further on we shall permanently use a special “reduction principle”111”(1)” The term is new.. It is easy to see that our main problem will be solved if we prove it for some infinitely dimensional subspaces of $A_{0}$ and $A_{1}$. Indeed, if the embedding of given spaces is compact, it remains such for any smaller parts. Similarly, if the sequences of norms $\|x_{n}\|_{A}$ and $\|x_{n}\|_{B}$ are equivalent, this equivalence is kept for corresponding norms of any subsequence $(x_{n_{j}})$. The “reduction principle” is intended for deleting all unnecessary parts of spaces (or sequences), because they may prevent from use of some important arguments in the forthcoming proofs.

The main advantage of the “reduction principle” in this paper is the
possibility to deal with bases of all needed subspaces. As known, a basis may
not exist even in a separable Banach spaces. At the same time, as shown in [6]
(Theorem 1.1, page 48), any Banach space has a basic sequence. Recall that a
sequence $(z_{n})$ in a Banach space $E$ is said to be basic one if $(z_{n})$
is a Schauder basis of $[z_{n}]$, where $[z_{n}]$ means the closed linear
subspace of $E$ spanned by the sequence $(z_{n})$. (By the way, the books [5]
and [6] by I. Singer will be our main reference for all needed properties of
the bases and basic sequences.) In conclusion: the “reduction principle”
allows us to replace in future proofs any considered space $E$ by a suitable
subspace $[z_{n}]$, obtaining a genuine basis instead of a basic sequence.

Yet more strong is an assertion from [6] (Corollary 1.5) about existence of a
basic subsequence in arbitrary sequence, having infinite dimension. In fact,
this Corollary asserts only existence of a so-named “block-basis sequence”,
but the previous volume [5] already explained on the page 66 that the block-
basis sequence is merely a special kind of basic sequences. Now it must be
clear why the infinite dimension of the sequence $(x_{n})$ was especially
stressed above, because only thus we may state (after application of the
“reduction principle”) that this sequence is a basis of the reduced space $A$.

Another useful possibility of the “reduction principle” is transformation of
any embedding $A\subset B$ into dense one, reducing the space $B$ to the
closure of $A$ in $B$. In our proof, this operation will be done for the space
$\Delta A=A_{0}\cap A_{1}$ which will be from now on regarded as dense in the
space $A$. This allows us to replace the sequence $(x_{n})$, defined above, by
a sequence $(y_{n})$ from $\Delta A$ which is so close to $(x_{n})$ as to have
equivalent norms in $A$ and $B$ as well. Moreover, due to [5] (Theorem 10.1,
page 93), the sequence $(y_{n})$ remains to be basis in $A$. Hence a new
sequence completely replaces the former one, but, for convenience, we proceed
to use the same notation $x_{n}$ instead of $y_{n}$, adding only one new
property that all $x_{n}$ belong to $\Delta A$.

By the definition of $\Delta A$, the sequence $(x_{n})$ geometrically (as set)
is the same in all three spaces $A,A_{0},A_{1}$, but the norms of elements may
be different. However we may change these norms unless this involves any
serious alteration of the initial problem. For instance, we may take all norms
$\|x_{n}\|_{A_{0}}=\|x_{n}\|_{A_{1}}=1$ and correspondingly obtain (due to
interpolation) some new values of $\|x_{n}\|_{A}\lesssim\|x_{n}\|_{\Delta
A}=\max\\{\|x_{n}\|_{A_{0}},\|x_{n}\|_{A_{1}}\\}$ 222”(2)” As usual, the sign
$\lesssim$ means an inequality with unknown coefficient like $a\leq kb$.. It
looks like multiplying all previous norms $\|x_{n}\|_{A}$ by some multipliers
$\lambda_{n}$, bounded from above on the whole. Moreover, the sequence
$(\|x_{n}\|_{A})$ proceeds to be bounded from below due to its non-compactness
in the space $B$ as was explained above while defining this sequence. Notice,
in addition, that $A$, as any interpolation space, is intermediate in the
couple $(A_{0},A_{1})$, therefore the sequence $(x_{n})$ cannot become
unbounded in $A$ even obtaining new (bounded) norms in $A_{0},A_{1}$. Indeed,
the linear independence of the elements $x_{n}$ with different indices implies
that $\|x_{n}\|_{A_{0}+A_{1}}=\min\\{\|x_{n}\|_{A_{0}},\|x_{n}\|_{A_{1}}\\}$
while $\|x_{n}\|_{A}\gtrsim\|x_{n}\|_{A_{0}+A_{1}}$. Therefore the sequence of
multipliers $(\lambda_{n})$ is bounded both from above and from below and, by
Definition 3.2 and Theorem 3.2 from [5], pages 21@-22, $(x_{n})$ remains a
bounded basis of the space $A$ with the same topology. By the way, the norms
$\|x_{n}\|_{B}$ obtain the same multipliers as the norms $\|x_{n}\|_{A}$, and
both norms remain equivalent.

Let us mention two important details concerning the “reduction principle”.
Excluding some elements $(x_{n})$ from one of spaces, we should simultaneously
exclude them from two other spaces, having thus the same remaining sequence
$(x_{n})$ in any of spaces at any time. The second remark is that we do not
change the notations after any such actions as if we had all these improved
objects from the very beginning. This concerns the spaces $A_{0},A_{1},A$ and
$B_{0},B_{1},B$ themselves as well.

After reduction of the sequence $(x_{n})$ in the space $A$ such that it became
a basis, we begin processing it in the spaces $A_{0}$ and $A_{1}$. Being a
basis, this sequence is infinite dimensional and remains such in other spaces,
because this property is algebraical and does not depend on topology.
Therefore we can reduce it till a genuine basis in the space $A_{0}$. At last,
by the next reduction, we could get an analogous basis in the space $A_{1}$.
As shown in [5] (Proposition 4.1, page 26), all previous bases remain be such
even after reduction, so that we obtain a common basis $(x_{n})$ in all three
spaces.

The properties of the elements $x_{n}$ in the spaces $B,B_{0},B_{1}$ can be
obtained as consequences of the given embeddings. Without loss of generality
we may suppose that all embeddings are normalized, namely, that

$\|x\|_{B_{0}}\leq\|x\|_{A_{0}},\quad\|x\|_{B_{1}}\leq\|x\|_{A_{1}},\quad\|x\|_{B}\leq\|x\|_{A}$
$None$

for all admissible $x$.

###### Lemma

Let the embedding $A_{1}\hookrightarrow B_{1}$ be compact and let $(x_{n})$ be
a basis of the space $A_{1}$ with unit norms. Then
$\lim_{n\to\infty}\|x_{n}\|_{B_{1}}=0$.

###### Demonstration Proof

Suppose, on the contrary, that $\|x_{n}\|_{B_{1}}\not\rightarrow 0$. Then
there exist infinitely many elements $x_{n_{j}}$ with norms in $B_{1}$ bigger
than some positive number $\varepsilon_{0}$. Due to (2), these norms are less
than $\|x_{n_{j}}\|_{A_{1}}=1$, so that the sequence $(x_{n_{j}})$ has
equivalent norms in the spaces $A_{1}$ and $B_{1}$. But, as shown in [4]
(Lemma 4.1 and Theorem 4.2, page 324), this contradicts to compactness of the
embedding $A_{1}\hookrightarrow B_{1}$.

A small remark: Lemma 4.1 from [4] requires that the sequence $(x_{n_{j}})$
contains a basic subsequence in $B_{1}$. But this sequence (geometrically,
without comparing the norms) is a part of the basis in $A_{1}$ and thus has an
infinite dimension. ∎

3. For the next application of the “reduction principle”, we construct a special subsequence $(x_{n_{j}})$ of the sequence $(x_{n})$ with the property $\|x_{n_{j+1}}\|_{B_{1}}\leq\|x_{n_{j}}\|_{B_{1}}/2$ for all $j=1,2,\dots$ Due to Lemma, such a subsequence necessarily exists. Making sufficient repetitions, we obtain

$\|x_{n_{j+k}}\|_{B_{1}}\leq 2^{-k}\|x_{n_{j}}\|_{B_{1}}\quad\text{for
any}\quad j,k\in\mathbb{N}.$ $None$

Due to “reduction principle”, we may use now only the sequence $(x_{n_{j}})$,
which keeps all needed properties of $(x_{n})$: it is basic in all three
spaces $A,A_{0},A_{1}$ (as subsequence of bases) and has equivalent norms in
the spaces $A$ and $B$. This allows us to return for this sequence to the
previous notation $(x_{n})$. The only novelty of the sequence $(x_{n_{j}})$,
that could be lost, is the formula (3). In former notations (without duple
indices), it can be rewritten as

$\|x_{n+k}\|_{B_{1}}\leq 2^{-k}\|x_{n}\|_{B_{1}}\quad\text{for any}\quad
n,k\in\mathbb{N}.$ $None$

As a last component of proof, we use the connection between basis expansion
and its partial sums ([5], Theorem 7.1, page 57). Namely, if $(x_{n})$ is a
basis in a Banach space $A_{1}$ and $a_{n}$ are the numerical coefficients,
then there exists a constant $C$ such that, for any $N$ and any $(a_{n})$, one
has

$\|\sum_{n=1}^{N}a_{n}x_{n}\|_{A_{1}}\leq
C\|\sum_{n=1}^{\infty}a_{n}x_{n}\|_{A_{1}}.$ $None$

In particular, it follows from this that

$\|a_{k}x_{k}\|_{A_{1}}=\|\sum_{n=1}^{k}a_{n}x_{n}-\sum_{n=1}^{k-1}a_{n}x_{n}\|_{A_{1}}\leq
2C\|\sum_{n=1}^{\infty}a_{n}x_{n}\|_{A_{1}}$ $None$

and

$\|\sum_{n=N}^{\infty}a_{n}x_{n}\|_{A_{1}}=\|\sum_{n=1}^{\infty}a_{n}x_{n}-\sum_{n=1}^{N-1}a_{n}x_{n}\|_{A_{1}}\leq(C+1)\|\sum_{n=1}^{\infty}a_{n}x_{n}\|_{A_{1}}.$
$None$

Let us notice that the same inequalities are hold after replacing $A_{1}$ by
$A_{0}$. Moreover, since the basis $(x_{n})$ is common for both spaces, the
constant $C$ depends here only on spaces $A_{0},A_{1}$ themselves and can be
chosen the same (maximal of two) for either of them.

4. Now, after all preliminaries, we can pass to the core of the proof. First of all, remark that both initial suppositions on compactness of embedding $A_{1}\hookrightarrow B_{1}$ and on equivalence of norms of the sequence $(x_{n})$ in spaces $A$ and $B$ remained true after all applications of the “reduction principle”. This allows us to retain the same notations of all spaces after those reductions and to use for our proof all set of inequalities (2)–(7).

The inequality (1) needs a special discussion, because it relates to all
spaces in their initial form, before all reductions. In order to make a bridge
between former and current states of all spaces and sequences, we define an
operator $Q$, acting on the initial space $A_{0}+A_{1}$ and equal to zero at
all elements, deleted during all reductions. For the remaining elements, we
set $Qx=x$. In fact, $Q$ is a projection operator of $A_{0}+A_{1}$ onto the
last subspace $[x_{n}]$, spanned by the remains of the sequence $(x_{n})$
after all reductions. Combining this operator with the embedding operator $J$,
we obtain all corresponding reductions for the space $B_{0}+B_{1}$. In the
same manner we obtain that $TQ:A_{0}+A_{1}\to B_{0}+B_{1}$ for any operator
$T$ which is defined only on reduced couples. This allows us to use the
inequality (1) for initial couples, replacing $T$ by $TQ$, or to use this
inequality without $Q$ for the same couples, obtained after reductions.

###### Demonstration Proof of the Main Theorem

In the following proof all spaces are considered in the final form, after all
reductions. We also need a special kind of operator-remainders that are very
useful in the theory of bases. Namely, if $x=\sum_{n=1}^{\infty}a_{n}x_{n}$,
then $R_{n}x:=\sum_{k=n}^{\infty}a_{k}x_{k}$. Next we recall the embedding
operator $J:A_{0}+A_{1}\to B_{0}+B_{1}$ and define the operators
$P_{n}=R_{n}J:A_{0}+A_{1}\to B_{0}+B_{1},\ n=1,2,\dots$ Due to presence of the
embedding operator, we obtain that $P_{n}:A_{0}\to B_{0}$ and $A_{1}\to B_{1}$
separately, that is, these operators can be interpolated between couples
$(A_{0},A_{1})$ and $(B_{0},B_{1})$.

Let us start with embedding $A_{1}\hookrightarrow B_{1}$. Consider

$\|P_{n}\|_{A_{1}\to B_{1}}=\sup_{\|x\|_{A_{1}}\leq 1}\|P_{n}x\|_{B_{1}}.$

If $x=\sum_{n=1}^{\infty}a_{n}x_{n}$ then, while computing the norms of
$P_{n}$, we may regard the norm of this sum less than (or equal to) 1. The
inequality (6) gives thus that $\|a_{k}x_{k}\|_{A_{1}}\leq 2C$ for any $k$.
But, as was proposed from the very beginning, $\|x_{k}\|_{A_{1}}=1$ for all
$k$, therefore $|a_{k}|\leq 2C$ also for any $k$. Returning to the operators
$P_{n}$, we obtain by (4) that, for every $x$ with $\|x\|_{A_{1}}\leq 1$, one
has

$\|P_{n}x\|_{B_{1}}=\|\sum_{k=0}^{\infty}a_{n+k}x_{n+k}\|_{B_{1}}\leq
2C\sum_{k=0}^{\infty}\|x_{n+k}\|_{B_{1}}\leq
2C\|x_{n}\|_{B_{1}}\sum_{k=0}^{\infty}2^{-k}.$ $None$

Consequently, $\|P_{n}\|_{A_{1}\to B_{1}}$ tends to zero as $n\to\infty$ due
to properties of the sequence $\|x_{n}\|_{B_{1}}$.

The estimation of $\|P_{n}\|_{A_{0}\to B_{0}}$ can be done, using inequality
(7) with $A_{1}$ replaced by $A_{0}$. We get

$\|P_{n}\|_{A_{0}\to B_{0}}=\sup_{\|x\|_{A_{0}}\leq
1}\|\sum_{k=n}^{\infty}a_{k}x_{k}\|_{B_{0}}\leq(C+1)\sup_{\|x\|_{A_{0}}\leq
1}\|\sum_{k=1}^{\infty}a_{k}x_{k}\|_{A_{0}}$ $None$

(the inequality appears due to embedding $A_{0}\hookrightarrow B_{0}$). The
last sum in (9) is exactly the norm of $x$ in $A_{0}$, therefore
$\|P_{n}\|_{A_{0}\to B_{0}}\leq C+1$ as required for interpolation (recall
that the inequalities (5)–(7) are independent of the coefficients $a_{k}$ and
we may consider these numbers in (8) and (9) as coordinates of $x$ in
different spaces $A_{1}$ and $A_{0}$).

For the end of proof, it is enough to use the condition (1) with $T=P_{n}$,
which gives that the norms $\|P_{n}\|_{A\to B}$ tend to 0 like
$\|P_{n}\|_{A_{1}\to B_{1}}$. Recall that the sequence $(x_{n})$ is bounded in
$A$ by definition. Set $\sup\\!\|x_{n}\|_{A}=K$. Then

$\|x_{n}\|_{B}=\|P_{n}x_{n}\|_{B}\leq\|P_{n}\|_{A\to B}\|x_{n}\|_{A}\leq
K\|P_{n}\|_{A\to B}\rightarrow 0\quad\text{as}\ n\to\infty.$

Consequently, we get that the sequence $(\|x_{n}\|_{B})$ cannot be equivalent
to the sequence $(\|x_{n}\|_{A})$. This contradiction proves the Main Theorem.
∎

Remark. The same proof is applicable to proving interpolation of the “two-
sided” compactness of linear operators without inequality (1). It is enough to
show that $\|P_{n}\|_{A_{0}\to B_{0}}\rightarrow 0$ like the case of spaces
$A_{1},B_{1}$ and to use the inequality $\|T\|_{A\to
B}\lesssim\max\\{\|T\|_{A_{0}\to B_{0}},\|T\|_{A_{1}\to B_{1}}\\}$ from the
definition of any interpolation functor.

Appendix (in accordance with Proposition 1 of [1]). Let $T$ be an arbitrary
linear operator, acting continuously from $A_{0}$ to $B_{0}$ and compactly
from $A_{1}$ to $B_{1}$. Define two spaces $Y_{i}\subset B_{i}\ (i=0,1)$
consisting of all $y=Tx,\ x\in A_{i}$, with norm
$\|y\|_{Y_{i}}=\inf\bigl{\\{}\|x\|_{A_{i}}\ :\ y=Tx\bigr{\\}}$. As known,
every such a space is called image of $T$ in the corresponding space $Y_{i}$
and is a Banach space. Present now $T$ as a composition $T=JS$, where the
operator $S$ is defined by $Sx=Tx$ for all $x\in A_{0}+A_{1}$ but considered
as a bounded operator from $A_{i}$ to $Y_{i},\ i=0,1$. Consequently $J$ will
be the embedding from $Y_{i}$ into $B_{i}$ for the same $i=0,1$. Applying the
functor $\Cal{F}$, we obtain that $S$ acts boundedly from
$\Cal{F}(A_{0},A_{1})$ into $\Cal{F}(Y_{0},Y_{1})$ by standard interpolation
theorems. At the same time, $J$ appears to be compact as an operator from
$Y_{1}$ into $B_{1}$ due to compactness of the operator $T$ and thus it is
compact as embedding from $\Cal{F}(Y_{0}.Y_{1})$ into $\Cal{F}(B_{0},B_{1})$
in virtue of the Main Theorem, proved above. In result, $T$ is also compact as
an operator from $A$ to $B$.

## References

  * 1 M. Cwikel, N. Krugljak, M. Mastyło, On complex interpolation of compact operators, Illinois J. Math. 40 (1996), 467–476.
  * 2 G. G. Lorentz, T. Shimogaki., Interpolation theorems for the pairs of spaces ($L^{p},L^{\infty}$) and ($L^{1},L^{q}$), Trans. Amer. Math. Soc. 159 (1971), 207–221.
  * 3 F. Cobos, L. M. Fernández-Cabrera and A. Martínez, Compact operators between K- and J- spaces, Studia Math. 166 (1989), 199–220.
  * 4 F. Cobos, Luz M. Fernández-Cabrera, Antón Martínez, E. Pustylnik, Some interpolation results that are the exclusive property of compact operators, Proc. Royal Soc. Edinburgh 132A (2002), 317–328.
  * 5 I. Singer, Bases in Banach spaces, Vol. I, Springer, 1970.
  * 6 I. Singer, Bases in Banach spaces, Vol. II, Springer, 1981.


# SOMONITOR: Explainable Marketing Data Processing and
Analysis with Large Language Models

Qi Yang<EMAIL_ADDRESS>ITMO UniversitySaint PetersburgRussia ,  Sergey
Nikolenko<EMAIL_ADDRESS>ITMO UniversitySteklov Institute of
MathematicsSaint PetersburgRussia ,  Marlo Ongpin<EMAIL_ADDRESS>SoMin.ai
ResearchKuala LumpurMalaysia ,  Ilia Gossoudarev<EMAIL_ADDRESS>ITMO
UniversitySaint PetersburgRussia ,  Yu-Yi Chu-Farseeva<EMAIL_ADDRESS>SoMin.ai
ResearchSingaporeSingapore and  Aleksandr Farseev<EMAIL_ADDRESS>SoMin.ai
Research, ITMO UniversitySingaporeSingapore

###### Abstract.

Online marketing faces formidable challenges in managing and interpreting
immense volumes of data necessary for competitor analysis, content research,
and strategic branding. It is impossible to review hundreds to thousands of
transient online content items by hand, and partial analysis often leads to
suboptimal outcomes and poorly performing campaigns. We introduce an
explainable AI framework _SOMONITOR_ that aims to synergize human intuition
with AI-based efficiency, helping marketers across all stages of the marketing
funnel, from strategic planning to content creation and campaign execution.
_SOMONITOR_ incorporates a CTR prediction and ranking model for advertising
content and uses large language models (LLMs) to process high-performing
competitor content, identifying core content pillars such as target audiences,
customer needs, and product features. These pillars are then organized into
broader categories, including communication themes and targeted customer
personas. By integrating these insights with data from the brand’s own
advertising campaigns, _SOMONITOR_ constructs a narrative for addressing new
customer personas and simultaneously generates detailed content briefs in the
form of user stories that can be directly applied by marketing teams to
streamline content production and campaign execution. The adoption of
_SOMONITOR_ in daily operations allows digital marketers to quickly parse
through extensive datasets, offering actionable insights that significantly
enhance campaign effectiveness and overall job satisfaction.

Digital Advertising, Ads Performance Prediction, Deep Learning, Large Language
Model, Explainable AI

††isbn: 978-1-4503-XXXX-X/18/06††ccs: Information systems Multimedia and
multimodal retrieval††ccs: Information systems Computational advertising

Figure 1. General pipeline of the _SOMONITOR_ advertising analysis framework.

General pipeline of the _SOMONITOR_ advertising analysis framework.

##  1\. Introduction

The contemporary online marketing landscape is bursting with an overwhelming
amount of content in the form of databases of advertisements, marketing
campaigns of various competitors, properties of user audiences, and more.
Marketers must not only sift through this information but also extract
meaningful insights regarding audience segmentation, trending topics, and
customer needs.

Recent advances in the field of large language models (LLMs) have brought them
to the fore as the tools of choice in various domains (see Section 2). These
models, trained on huge datasets, exhibit remarkable capabilities in both
content analysis and content generation. In online marketing, modern LLMs are
already able to offer a promising solution by processing and analyzing large
datasets to identify key elements, facilitating a more targeted and effective
marketing strategy. Moreover, they can help generate new advertisement
content, both text-based and multimodal.

Despite all this progress, in this work we note that vanilla LLMs also have
limitations in _content scoring_ , which is a crucial aspect of effective
marketing. We show that a system specifically tailored for CTR prediction
based on advertising content performs better at content scoring than standard
LLMs, even those enhanced with multimodal capabilities, offering a more
reliable tool for marketers.

Therefore, we propose a system, called _SOMONITOR_ , that combines predictive
analytics and LLMs in a unified online marketing assistant. Importantly,
marketing strategies encompass more than just data analysis; they involve
understanding and implementing effective communication styles. It is essential
to utilize these communication styles not merely as classification labels but
as dynamic personas. This approach enables the identification of different
communication schemas tailored to diverse user personas. These schemas, and
the user personas themselves, can be analyzed in existing marketing campaigns
via a clustering procedure (Section 4). The next step involves aligning these
personas with appropriate communication styles to craft compelling narratives.
These narratives, or _stories_ , are essential content that marketers can
directly employ in their campaigns. However, to construct these stories one
has to use high-quality data, including marketing communications and
advertisements that have previously proven to be successful in building
rapport with the corresponding user personas.

Thus, the core issue circles back to the need for an advanced predictive model
for content scoring, presented in Section 5. This model can be used to filter
and identify “good” advertisements that can then serve to enhance the
efficiency of LLMs in generating impactful marketing content. Our research
addresses this need by introducing a predictive model that refines data input
for LLMs, ensuring the generation of content that resonates well with target
audiences and supports strategic marketing initiatives; in Section 6, we show
how this model fits together with an LLM in a unified workflow that can
generate complete user stories. The overall pipeline of _SOMONITOR_ is
illustrated in Fig. 1.

The paper is organized as follows: Section 2 surveys related work, in Section
3 we discuss LLM-based extraction of content pillars, Section 4 introduces
persona and theme identification, Section 5 discusses content scoring, Section
6 introduces the story generation process, and Section 7 concludes the paper.

##  2\. Related work

The all-encompassing success of LLMs has made them into a tool of choice for
many applications (Makridakis et al., 2023; Minaee et al., 2024). Modern LLMs
are able to perform a wide variety of tasks, from low-resource machine
translation (Enis and Hopkins, 2024) to writing source code for full-scale
applications (et al., 2021, 2023) and solving problems that require both
mathematics and engineering design (Kevian et al., 2024). Importantly, there
has been a growing body of research devoted to overcoming the quadratic
complexity bottleneck inherent in the original Transformer architecture
(Vaswani et al., 2017). Approaches include sparse attention mechanisms
(Beltagy et al., 2020; Child et al., 2019), low-rank decomposition of
attention weight matrices (Wang et al., 2020; Choromanski et al., 2022), and
various modifications that combine self-attention with recurrent architectures
which have inherently linear complexity (Ma et al., 2023; Orvieto et al.,
2023). As a result, latest LLMs can extend their context windows (i.e., input
sizes) up to millions of tokens (Team, 2024; Anthropic, 2024), which makes it
possible to use LLMs directly for mid- and large-scale analysis of text
datasets.

Recently, large language models have also obtained multimodal capabilities.
They have been successfully used for video understanding (Tang et al., 2024),
and the recently released GPT-4o, where ’o’ stands for “Omni”, brings seamless
multimodality of image, audio, and video analysis to state-of-the-art LLMs
(OpenAI, 2024). Moreover, LLMs can be combined with diffusion-based generative
models (Ho et al., 2020; Song et al., 2021; Rombach et al., 2022) to achieve
state-of-the-art image and video generation capabilities (Ho et al., 2022;
Hong et al., 2022; Liu et al., 2024).

Being able to interpret data through human-perceivable dynamic categories,
such as topics or audiences, represents a significant step towards explainable
AI. Nonetheless, the sheer volume of content and its prioritization continue
to pose challenges, with limitations inherent in LLMs, in particular related
to their hallucination phenomena (Zhang et al., 2023). For instance, if a
marketer understands that the primary audience for 1000 pieces of marketing
content is “families”, but lacks data on the content’s popularity across this
audience, such insights are not actionable for making informed decisions. At
the same time, given a ranking task, LLMs always come up with different
responses in consequent runs (Chen et al., 2023). At the same time, platforms
dedicated to online content dissemination, such as social networking and
search engine platforms, namely _Facebook_ (_Meta_) (He et al., 2014),
_Google_ (McMahan et al., 2013), _Alibaba_ (Ouyang et al., 2019), and _Taobao_
(Ge et al., 2018), have invested considerable efforts towards content
prioritization and scoring. Unfortunately, these advancements are based on
private datasets and are typically inaccessible to external content creators,
including digital marketers. Proprietary engagement data, crucial for refining
content scoring models, remains exclusive to these platforms, thereby
hindering independent creators from accurately predicting or enhancing the
efficacy of their content.

From all the above, it is evident that the comprehensive capabilities of LLMs
position them as high-level assistants across a myriad of tasks within the
realm of online marketing. However, there exist relatively few research papers
devoted to these potential applications (Feizi et al., 2024). The marketing
industry is currently only starting to incorporate LLMs into the workflows,
with many recent whitepapers and business surveys of possible applications,
problems, and potential breadth of adoption of LLMs (Thackray and Northin,
2023; Keni and ElBermawy, 2024). Our recent work (Yang et al., 2023) presented
a comprehensive online marketing analysis system based on large language
models; in this paper, we build upon this work and combine and further improve
LLM-based analysis with predictive analytics. A key advantage noted in (Yang
et al., 2023) was the fact that LLM answers are understandable for humans and
actionable in terms of business results: LLMs such as GPT-3.5 (Ouyang et al.,
2022) and GPT-4 (OpenAI, 2023) were already able to explain the “reasoning”
behind recommender models and provide aggregate insights about advertising
campaigns. Before LLMs, text corpora in the context of recommender systems had
been aggregated via topic modeling (Koltcov et al., 2014; Nikolenko, 2015),
sometimes also with deep learning (Tutubalina and Nikolenko, 2018) and user
profiling (Buraya et al., 2018; Tutubalina and Nikolenko, 2017), but topic
modeling is based on the bag-of-words assumption and cannot summarize text as
an LLM does. Visual understanding of ads has also been explored with
convolutional networks (Savchenko et al., 2020).

However, a robust technology that enables effective differentiation of content
sources for insight extraction, as well as a cohesive framework for data
exploration that integrates both content differentiation and LLM-based
explanations, is still sorely needed. Our work aims to address these gaps by
developing methods that enhance the functionality of LLMs in online marketing
applications, facilitating more efficient utilization of modern AI in real-
world scenarios.

##  3\. Content pillar identification

As noted above, data handlers in performance marketing frequently encounter
large volumes of creative assets to analyze, along with numerous ongoing
promotional activities from competitors in an “always-on” environment. Given
this context, conducting detailed analyses for each advertisement or even for
every specific competitor campaign becomes impractical, highlighting the need
for automated analytical tools. These tools are crucial for assisting
marketers in quickly assimilating, synthesizing, and driving inferences from
extensive data and information available to them.

To address this challenge, we propose to integrate a novel method into our
framework that leverages large language models (LLMs) to provide semantic
insights into content, referred to as “content pillars” below. We outline an
analytical pipeline that incorporates explanations and generations based on
LLMs, demonstrating its practical utility through an empirical scenario
involving four Singapore-based telecommunication companies. This component of
our framework aims to enhance the interpretability and understanding of data,
thereby supporting more informed decision-making in these dynamic and
competitive sectors.

The architecture of our analytic process is illustrated in Fig. 2. Initially,
we employ an LLM to extract specific, well-defined insights from the input
content, such as the customer needs addressed by the advertisement and the
products being advertised. These insights are then archived as content pillars
in a tabular format. Subsequently, these pillars are utilized alongside
custom-crafted prompts to perform a generalized analysis of a brand’s target
demographics, personas, needs, and insights conveyed by the advertisements, as
well as the tone and topical categories of both current and previous
campaigns. This comprehensive analysis mirrors the campaign assessments
typically conducted by marketing professionals and can be further used to
refine a brand’s messaging, tone, and target demographics. Below we explore
these elements in detail.

Figure 3 presents sample qualitative results of our experiments on the
analysis of content pieces. We curated batches of advertisements from the
_Facebook Ad Library_ related to the same brand and processed them through an
LLM. The processing was uniquely tailored through natural language prompt
engineering. As a result, the LLM successfully identified key attributes of
each advertisement, providing adept responses to ostensibly “human” inquiries
such as pinpointing the human need, insight, and predominant archetypes in a
specific ad. Notably, responses to most queries are standardized (as directed
by the prompt) and amenable to automated processing. This type of analysis has
always been pivotal in online marketing, and to our knowledge, it has not been
effectively automated and scaled until now, traditionally requiring human
intervention and thus being limited to a select number of advertisements
rather than an extensive dataset.

Figure 2. General pipeline of our LLM-based analysis Figure 3. Sample ad
analysis

##  4\. Communication Persona and Theme Identification

###  4.1. Problem setting

In the field of marketing, utilizing explainable data descriptors such as the
content pillars is essential. However, to significantly enhance a brand’s
marketing and communication strategies it is necessary to go beyond mere
description and engage in inferential data analysis. Unfortunately, marketers
often lack the necessary skills in data operations, hindering their ability to
derive meaningful conclusions from the data, thereby requiring additional
support. To bridge this gap, we propose a unified framework _SOMONITOR_ that
unites LLM-based analysis with content scoring.

_SOMONITOR_ is designed to provide marketers with higher-level content
observations.

In marketing, the narrative constructed by any content emerges from an
underlying story, which is a synthesis of a communication theme and a specific
customer persona that the campaign aims to engage. We will come back to the
stories in Section 6, illustrating this concept through a representative
example, highlighting the integral relationship between the storytelling
elements and the targeted persona. This approach empowers marketers to craft
more resonant and effective communication strategies by aligning their
messaging with the expectations and needs of their intended audiences. But to
get to a good story, we need to extract two essential storytelling components:
personas and challenges.

###  4.2. Persona Identification

In marketing, the customer persona is best developed based on data about the
audience of a brand, supported by other content pillars such as customer
needs, interests, and aspirations (Malik, 2019). We have employed a commonly-
used clustering algorithm X-Means (Pelleg et al., 2000) to cluster the content
pieces into distinct customer personas based on the content from the brands,
identifying the number of clusters automatically via Bayesian Information
Criterion values (Pelleg et al., 2000). Clustering has been performed over the
ADA embeddings, a state of the art representation learning model for text
(Neelakantan et al., 2022), of the “Audience” content pillar as the main
semantic component differentiating the data. X-Means was run with $3$ starting
centroids and $k_{\max}=50$.

For this study, we analyzed data from the Gojek car-hailing brand and its main
competitor in Singapore, _Grab_ , focusing exclusively on the B2B business
audience to limit the number of personas. The data for this experiment,
collected over 2023 and 2024, comprised $5{,}967$ content pieces, with
$3{,}703$ published as ads and $2{,}264$ as organic social media posts. Since
most of the content related to B2B product offerings for both brands was
presented in ads, we focused solely on the advertising content, totaling
$1{,}120$ ads related to business products. Brand-wise, _Gojek_ ran the
majority of the ads ($76.8$%, or $849$ ads), while _Grab_ accounted for the
remaining $23.2$% ($271$ ads).

Figure 4. Sample persona analysis results

After detecting each cluster, we annotated them and generated parameters such
as cluster name and cluster description by prompting an LLM to do so based on
the predominant parameters and content of the posts associated with each
cluster. Finally, an image for each persona was generated by the LLM in
accordance with the persona’s description. As shown in Fig. 4, we identified
three distinct clusters, each representing a unique customer persona along
with their associated characteristics: “Efficiency Enthusiasts” (Persona 1),
“Financial Empowerment Champions” (Persona 2), and “Efficiency Innovators”
(Persona 3), with content counts of $206$, $144$, and $707$ respectively. Note
that some content items did not correspond to any of the three identified
personas (i.e., represented outliers) and were thus excluded from the final
tally, explaining the disparity with the initial $1{,}120$ ads.

As a result, notable distinctions between the personas have emerged. Both
Persona 1 and Persona 3 focus on organizational efficiency, albeit through
different approaches: Persona 1 advocates for efficiency through traditional
methodologies, while Persona 3 champions it through innovative strategies. In
contrast, Persona 2 stands apart by primarily emphasizing the need for
financial empowerment of employees.

###  4.3. Communication Theme: Challenges

A persona is an essential but not sufficient component needed to come up with
a marketing story and its corresponding content briefs. In particular, it is
important to identify a communication scheme to be combined with the persona’s
key attributes such as background or character, so that the story would get
proper context and would grab attention (Malik, 2019). To explore this, we
have made a further step towards clustering our data, but this time we have
performed X-Means clustering based on the “Insights” content pillar, again
using ADA embeddings for text (Neelakantan et al., 2022) and running X-Means
with $3$ starting centroids and $k_{\max}=50$.

Figure 5. Sample challenges mined by our system

Similarly to persona clustering, we annotated the resulting challenge clusters
and generated parameters such as cluster name and cluster description by
prompting an LLM to do so based on predominant parameters and content of the
posts associated with each cluster. Figure 5 shows sample results: in this
case, we have identified three distinct clusters, each representing a unique
customer challenge along with their associated characteristics: “Inefficient
Corporate Expense and Transportation Management” (Challenge 1), “Improving
Business Operations and Employee Satisfaction” (Challenge 2), and
“Streamlining Work Transport Processes” (Challenge 3), with content counts of
$672$, $94$, and $336$ respectively.

##  5\. Content scoring

###  5.1. Problem setting and dataset

To render the recommendations generated by the system actionable, one has to
enable marketers to evaluate data and select which content to incorporate into
analytics, ideally based on anticipated performance. This leads to the need
for content scoring, so in this section we add to _SOMONITOR_ a system for the
scoring of advertising content, developed in our previous work (Yang et al.,
2023), and evaluate it against state of the art LLMs to prove its continued
relevance.

Brand | nDCG@5 | nDCG@10 | Recall@3 | Recall@5
---|---|---|---|---
A | 0.498 | 0.796 | 0.333 | 0.4
B | 0.541 | 0.821 | 0.333 | 0.4
C | 0.588 | 0.829 | 0.6 | 0.6
Table 1. Experimental results for _SOMONITOR_. | nDCG@5 | nDCG@10 | Recall@3 | Recall@5
---|---|---|---|---
GPT4-gd | 0.591 | 0.818 | 0.333 | 0.6
GPT4 | 0.465 | 0.755 | 0 | 0.4
GPT4o-gd | 0.599 | 0.827 | 0.333 | 0.6
GPT4o | 0.511 | 0.750 | 0.333 | 0.4
Gemini-gd | 0.578 | 0.817 | 0.333 | 0.6
Gemini | 0.564 | 0.769 | 0 | 0.6
_SOMONITOR_ | 0.588 | 0.829 | 0.6 | 0.6
Table 2. Performance evaluation against LLM baselines; “gd” represents a
grounded model.

To assess the effectiveness of our recommender system, we conducted a
validation study using real ad creatives and their performance data. We
collected real-world ad creatives and their performance data from three brands
on _Facebook_ , each with distinct marketing objectives: sales, conversion,
and traffic, spanning from October 1, 2023 to December 31, 2023. The dataset
comprised text and images of their ads alongside their performance measured as
CTR values. We chose three (anonymized) brands: Brand A (16 ads in the fitness
industry), Brand B (29 ads in the education industry), and Brand C (16 ads in
the automobile industry).

The ads were assessed not just according to the brand affiliation, but also
according to the Ad objective selected on the Meta Ads platform, which is a
crucial component of evaluation in our scenario due to the fundamental
differences in click-through rates across various industries and marketing
goals that Ads achieve with different Ad objective settings (Yang et al.,
2023). For instance, advertisements optimized for clicks may result in lower
costs per click and higher click-through rates, yet they may not effectively
convert customers. Conversely, ads aimed at achieving better conversion rates
might not exhibit as high click-through rates as those optimized merely for
clicks.

###  5.2. Content scoring models

For content scoring, we use our previously developed approach (Yang et al.,
2023). Although this model was originally designed for predicting CTR by
classifying advertisements into CTR performance categories, in this work we
operate in a recommendation problem setting, i.e., pose content scoring as a
ranking problem. This is because, first, marketers do not necessarily need
precise CTR values to choose the best content but rather a comparative
assessment, second, CTR values undergo significant distribution shift across
platforms, time, and other external factors, but the ranking of ads should be
more stable, and third, the LLM performance in qualitative ranking should be
significantly better than in numerical predictions, ensuring a more fair
comparison.

Thus, we take the SODA model from (Yang et al., 2023) that predicts a
distribution over “High CTR”, “Average CTR”, and “Low CTR” labels and add a
linear layer that translates the probabilities into a single score via a
trainable linear combination:

$\mathrm{Score}=\alpha\cdot
p(\mathrm{HighCTR})+\beta\cdot(1-p(\mathrm{HighCTR})).$

As a result, we convert a pretrained classification model into a ranking
model.

On the side of LLMs, we selected state of the art models GPT-4, GPT-4o, and
Gemini 1.5 Pro for comparison with _SOMONITOR_. GPT-4 and its optimized
version, GPT-4o, represent the latest advancements in the GPT series, known
for their robustness and versatility in handling diverse text-based and
multimodal tasks (OpenAI, 2023), while Gemini 1.5 Pro is a powerful model
developed by _Google_ and competing with OpenAI’s models successfully in many
benchmarks (Team, 2024).

However, a significant challenge in utilizing LLMs for this task is their
tendency to hallucinate, which can result in generating inaccurate or
nonsensical information that compromises the reliability of their output. To
mitigate this issue and ground the LLM-based approach to ensure the predicted
data was trustworthy, we implemented several measures to reduce randomness:

  * •

_temperature adjustment_ : we set the temperature parameter of the LLMs to
0.1, which is known to improve stability by reducing the variability in the
model’s outputs;

  * •

_grounding_ : to further mitigate randomness, we included another three
example advertisements from the brand within the prompt, each with a specified
CTR rank: one with the best performance, one with average performance, and one
with the worst performance;

  * •

_LLM Ensemble_ : inspired by ensemble methods, we conducted the ranking
process with LLMs five times using the same settings, and the final rankings
were determined by summing the rank positions of each advertisement from these
five runs and then ordering them from the lowest to highest total rank.

###  5.3. Results

For evaluation, we use standard ranking-based metrics. Specifically, we
measured Recall@3 and Recall@5 to gauge the model’s ability to retrieve
relevant items within the top 3 and top 5 recommendations; the recall metric
is very important in practice, especially in resource-constrained domains such
as online advertising campaigns. High Recall@$k$ ensures that top $k$
recommendations encompass a substantial portion of the truly relevant items,
which enables marketers operating under tight budgets to focus their efforts
on the most promising opportunities while minimizing the risk of overlooking
potentially valuable prospects. We have also computed normalized discounted
cumulative gain (nDCG) at cutoffs 5 and 10, another commonly used way to
assess ranking quality.

First, we present a case study in Table 1 that showcases the framework’s
performance across three major industries. In the fitness sector, _SOMONITOR_
achieved moderate effectiveness with nDCG@5 of 0.498 and nDCG@10 of 0.796,
alongside Recall@3 and Recall@5 scores of 0.333 and 0.4, respectively. Brand
B, representing education, showed improved performance, with nDCG@5 of 0.541
and nDCG@10 of 0.821, but recall stayed the same. In the automobile industry
results improved, achieving nDCG@5 of 0.588 and nDCG@10 of 0.829, with
recall@3 and recall@5 both scoring 0.6. These findings show that content
scoring quality varies across industries and highlight the importance of
industry-specific optimization to enhance recommendation accuracy.

Then we undertook a comparative evaluation of our _SOMONITOR_ framework
against LLM baselines. In campaigns focused on driving traffic, the primary
goal is to maximize click-through rates (CTR), which serve as a measure of
user engagement and interaction with the advertisement, which is particularly
pertinent given the distinctive challenges posed by traffic-driven campaigns
as opposed to conversion-oriented strategies. Thus, we evaluate the
performance with the data from Brand C, a traffic-oriented campaign. In Table
2, we present the evaluation result from a case study focused on Brand C,
comparing the performance of _SOMONITOR_ against modern large language models.

A key observation from Table 2 is the significant performance boost achieved
by incorporating knowledge grounding across various models and metrics. For
instance, the nDCG@5 score for GPT-4 improved from 0.465 without grounding to
0.591 with grounding, while its Recall@5 increased from 0.4 to 0.6. This trend
is consistent across other LLM baselines, such as GPT-4o and Gemini1.5 Pro,
underscoring the critical role of grounding in enhancing the relevance and
quality of recommendations. Ungrounded LLMs exhibit markedly lower
performance, particularly in the Recall@3 metric: both Gemini and GPT-4 failed
to place any high-performance items within their top $3$ results at all.

As a result, the prediction model outperforms LLMs in recommending relevant
items, achieving the highest nDCG@10 of 0.829 and recall@3 of 0.6 among the
compared models. This superior performance demonstrates _SOMONITOR_ ’s ability
to effectively balance ranking accuracy and item recall, delivering highly
relevant and stable (especially compared to individual LLM results)
recommendations to users. Notably, these outcomes are achieved without any
fine-tuning (grounding) using data from the actual industry-specific
distributions: we used a pretrained model. This offers significant potential
for further improvement of results should such fine-tuning be implemented, a
direction we intend to explore in our future work. Improvements in LLMs’
Recall@k due to grounding also hint at the critical role of domain knowledge
and context in enhancing the relevance and quality of recommendations.
Ungrounded LLMs, relying solely on their pre-trained language models, struggle
to capture the nuances and specifics of the recommendation task, resulting in
sub-optimal item retrieval. By incorporating domain-specific knowledge and
grounding the models in the relevant context, the recommendations become more
tailored and relevant.

We note that our proposed _SOMONITOR_ framework outperforms the baselines in
both Recall@3 and Recall@5, achieving a Recall@3 score of 0.6 which is higher
than any LLM’s result. This supports our conclusion that the online marketing
industry still cannot fully rely on LLMs for content scoring and explains our
decision to include a CTR prediction and ranking model into the mostly LLM-
based _SOMONITOR_ framework.

##  6\. Data-Driven Story Generation

Figure 6. User story generation: pipeline and an example.

In order to establish a data-driven narrative that would be useful, easy to
understand, and attractive to content marketing professionals, it is essential
to delineate the content and marketing strategies a brand may deploy, guided
by the analysis of the best-performing content from competitive brands. At
this point, we have already discussed how the _SOMONITOR_ framework extracts
personas and challenges based on advertising content prefiltered by a CTR
prediction and ranking model. Now it is time to combine them into a unified
marketing story.

Consider the scenario where we are part of a marketing team at _Gojek_ ,
tasked with identifying a suitable communication theme and a target persona
for a campaign aimed at market expansion through new audience engagement. It
is desirable to opt for a persona and theme that are presently underexploited,
thereby expanding our audience reach. As illustrated in Fig. 4, the analysis
shows that Persona 1, labeled “Efficiency Enthusiasts”, is more heavily
leveraged by _Grab_ than by _Gojek_ , indicating a potential niche opportunity
for _Gojek_. At the same time, as shown in Fig. 5, the communication theme
“Challenge 3: Streamlining Work Transport Processes” is more frequently
addressed by our competitor, _Grab_ , but is underrepresented in _Gojek_ ’s
content. This observation advocates for adopting this theme for persona-
centric narrative generation.

Consequently, adhering to the framework outlined in Figure 6, we prompt an LLM
to amalgamate the characteristics of the selected persona and the chosen
communication theme to devise a narrative for a fictitious character, “Samuel
Tan”, a business owner in Singapore. The pipeline for this generation is shown
in Figure 6: character description is also generated by a custom-prompted LLM,
and then the character and theme are combined to create a compelling story.
The story is abbreviated in Fig. 6, in reality it explains over several
paragraphs how Samuel prioritizes business efficiency but often neglects
employee satisfaction, leading to increased turnover rates. Recognizing this
issue, Samuel opts for _Gojek_ not merely as an efficiency solution but as a
means to reengage with employees, enhance their efficiency, and improve
overall job satisfaction; the story ends with a conclusion (emphasized in Fig.
6) that shows an important insight that Samuel has obtained by engaging with
_Gojek_. This narrative could serve as a content brief for a creative agency
or be utilized as a pitch for a novel marketing campaign, previously
unexplored by the marketing team in such depth and with such rapid production
capability. In our professional opinion, content briefs produced by
_SOMONITOR_ are on par with similar human-written narratives and can be used
just as effectively.

##  7\. Conclusion

In this work, we have introduced an innovative explainable AI framework
_SOMONITOR_ that aims to combine human intuition with the efficiency of modern
AI to significantly enhance the capabilities of marketers across all stages of
the marketing funnel, from strategic planning to content creation and campaign
execution. The challenges traditionally faced by marketers, especially the
need to manually sift through immense quantities of transient online content,
are addressed by _SOMONITOR_ ’s ability to automate and refine the process of
competitor analysis, content research, and strategic branding. _SOMONITOR_
ranks advertising content by its potential to achieve higher click-through
rates via a specially trained model and then employs LLMs to distill core
content pillars such as target audiences, customer needs, and product features
from successful competitor marketing endeavors. These pillars then lead to
communication themes and targeted customer personas, providing a structured
basis for content and campaign planning. By integrating these insights with
data from a brand’s own marketing campaigns, _SOMONITOR_ not only constructs
compelling narratives for new customer personas but also generates detailed
content briefs in the form of customer persona stories, empowering marketing
teams to produce content and execute campaigns. We believe that _SOMONITOR_
can transform digital marketing operations, enabling marketers to quickly
navigate through large datasets and derive actionable insights that boost
campaign effectiveness and enhance job satisfaction, redefining traditional
marketing approaches (Farseev, 2024).

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