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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <issn pub-type="ppub">1613-0073</issn>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>RAGSys: Item-Cold-Start Recom mender as RAG System</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Emile Contal</string-name>
          <email>emile@crossingminds.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Garrin McGoldrick</string-name>
          <email>garrin.mcgoldrick@crossingminds.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="editor">
          <string-name>Recommender systems, Information Retrieval, Large Language Models, Few-Shot Learning, In-Context-Learning</string-name>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Crossing Minds Inc</institution>
          ,
          <addr-line>San Francisco</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>Large Language Models (LLM) hold immense promise for real-world applications, but their generic knowledge often falls short of domain-specific needs. Fine-tuning, a common approach, can sufer from catastrophic forgetting and hinder generalizability. In-Context Learning (ICL) ofers an alternative, which can leverage Retrieval-Augmented Generation (RAG) to provide LLMs with relevant demonstrations for few-shot learning tasks. This paper explores the desired qualities of a demonstration retrieval system for ICL. We argue that ICL retrieval in this context resembles item-cold-start recommender systems, prioritizing discovery and maximizing information gain over strict relevance. We propose a novel evaluation method that measures the LLM's subsequent performance on NLP tasks, eliminating the need for subjective diversity scores. Our findings demonstrate the critical role of diversity and quality bias in retrieved demonstrations for efective ICL, and highlight the potential of recommender system techniques in this domain.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Large Language Models (LLMs) have emerged as a powerful
tool for natural language processing, demonstrating
remarkable abilities in areas like text completion, summarization,
and question answering [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. One of their most intriguing
capabilities is their potential to learn ”common sense” –
general knowledge about the world that allows them to
reason and make inferences beyond the literal meaning of
text. This has fueled excitement about the possibility of
achieving zero-shot learning, where LLMs can solve unseen
problems without any prior training on specific tasks [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>
        However, a crucial distinction exists between generic
public knowledge and the specific private knowledge required
for most real-world use cases. While LLMs excel at generic
text completion or chat-like interactions, practical
applications often demand solving specific and repeatable
downstream tasks within a particular domain [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. This typically
necessitates knowledge specific to a business or
organization, such as understanding internal processes, up-to-date
product details, or customer behavior.
      </p>
      <p>
        Fine-tuning, a technique where LLMs are trained on large
datasets tailored to the target task, ofers a path towards
adapting LLMs to these domain-specific needs. Yet,
finetuning presents significant challenges. When trained on
tasks-specific data, LLMs tend to forget knowledge and skills
gained in the initial training, a phenomenon referred to as
Catastrophic Forgetting [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. Consequently, a fine-tuned
LLM loses some of its ability to generalize to novel
examples that aren’t well represented in its fine-tuning training
data. Moreover, while fine-tuning allows an LLM to
memorize task-specific information, it doesn’t necessarily allow
the LLM to reason about that information [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. As a final
consideration, keeping LLMs constantly up-to-date using
ifne-tuning can be infeasible, especially for domains with
frequently changing information like e-commerce product
inventory, whereas it is easy to update a database in
realtime from which information is retrieved.
      </p>
      <p>
        As an alternative to fine-tuning, In-Context Learning
(ICL) ofers a promising approach for leveraging LLMs in
Information Retrieval’s Role in RAG Systems (IR-RAG) - 2024
∗Corresponding author.
†Both authors contributed equally to this research.
[
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]. We refer to [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ] for a recent survey on ICL.
      </p>
      <p>
        This paper focuses on few-shot learning and the retrieval
of relevant demonstrations for this process, where a
demonstration is some text which is included in the LLM’s context
to demonstrate how the LLM should formulate correct
answers. Few-shot learning presents a well-structured
problem, allowing us to evaluate the quality of the retrieval
algorithm using established classification metrics. Crucially,
we show that enriching a language model with a few-shot
example retriever ofers a powerful method to achieve
finetuning-like behavior, steering the output of the LLM towards
the desired outcome even with limited data. Interestingly,
increasing the context size in prompts beyond a certain
point yields diminishing returns. The most impactful
information resides within a relatively small set of well-chosen
demonstrations, rather than overloading the prompt with
vast amounts of data [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. This highlights the importance of
efective retrieval strategies, transforming  -shot learning
into a top- information retrieval problem at its core.
      </p>
      <p>
        Building upon this concept, this paper identifies
desirable properties for a RAG system under the framework of
few-shot learning. We demonstrate that state-of-the-art
retrieval systems in this context resemble item-cold-start
recommender systems. Unlike exact search algorithms that
prioritize precision and recall, our focus is on discovery, by
maximizing the set of collective information gain from the
retrieved demonstrations. This necessitates solving various
trade-ofs between query relevance, quality scoring, as well
as diversity algorithms to ensure a variety of informative
examples are surfaced. Furthermore, we propose a method
for evaluating RAG system performance through the
subsequent performance of the enriched LLM on established
NLP tasks like question answering or text generation. This
methodology ofers a valuable approach to directly
assessing diversity and quality-based retrieval systems, which
removes the need to define a subjective diversity score, a
historically challenging aspect of evaluating such systems
in academic settings [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ].
      </p>
      <p>CEUR</p>
      <p>ceur-ws.org</p>
      <p>To summarize, in this paper we study the impact of
diversity and quality bias in retrieving demonstrations for
ICL. We start by reviewing the use of diversity and other
biases in both ICL and Information Retrieval works. We
then propose a method for evaluating the performance of
diferent retrieval algorithms. Then we present experiments
and results demonstrating the impact of diversity and
quality bias on an LLM’s ability to generate correct answers.
Finally we discuss the applicability of state-of-the-art ICL
retrieval algorithms in real-world setting, and show that
recommendation engines ofer a better solution than semantic
search engines.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <p>This paper sits at the intersection of two distinct, but
increasingly intertwined, research areas: In-Context
Learning for Large Language Models and Information Retrieval.
While ICL focuses on enabling LLMs to learn from carefully
selected contextual information, IR deals with retrieving
relevant information from document collections. Our work
leverages concepts from both fields to address the challenge
of few-shot learning with LLMs.</p>
      <sec id="sec-2-1">
        <title>2.1. Few-Shot In-Context Learning with</title>
      </sec>
      <sec id="sec-2-2">
        <title>Retrieval Augmented Generation</title>
        <p>Within the context of RAG, few-shot learning can be defined
as a specific scenario where the ”documents” retrieved are
actually ”examples” used to guide the LLM. These examples
can also be referred to interchangeably as ”In-Context
Examples” (ICE) or ”demonstrations”. The importance of ICL
in achieving state-of-the-art LLM performance is
undeniable, with its ubiquitous presence in top benchmarks across
various domains. Consequently, ICL research is a rapidly
evolving field with numerous proposed algorithms.</p>
        <sec id="sec-2-2-1">
          <title>2.1.1. Pure Diversity</title>
          <p>
            Several noteworthy ICL approaches have emerged that
address the challenge of retrieving informative examples for
few-shot learning. Some methods only promote the
diversity of the demonstrations, like in [
            <xref ref-type="bibr" rid="ref11">11</xref>
            ] where the authors
utilize  -means clustering in a dense embeddings space to
achieve diversity. By applying  -means to the sentence
embeddings of the demonstrations, this approach ensures that
the retrieved examples cover a variety of semantic spaces,
inherently increasing the mutual information of the retrieved
set, but without taking into account the relevancy to the
query.
          </p>
        </sec>
        <sec id="sec-2-2-2">
          <title>2.1.2. Pure Quality</title>
          <p>
            Other approaches focuses on identifying examples where
the LLM exhibits low token-level uncertainty. In [
            <xref ref-type="bibr" rid="ref12">12</xref>
            ] the
authors analyze token probabilities within candidate 0-shot
prompts. By prioritizing prompts where the LLM has the
highest generation likelihood (low perplexity), this approach
aims to select examples that hold the potential for significant
learning gains for the LLM. The intuition that the authors
give is that a prompt that is more expected by the LLM is
more likely to help it extracting the relevant information.
Accessing the per-token probabilities for all examples incurs
a significant compute cost, but can be pre-computed as they
do not depend on the query.
Notably, a connection can be drawn between traditional
fulltext search algorithms and pure relevance approaches. In
[
            <xref ref-type="bibr" rid="ref13">13</xref>
            ] the authors use BM25 [
            <xref ref-type="bibr" rid="ref14">14</xref>
            ], a well-established retrieval
ranking function commonly used in information retrieval
tasks. This approach essentially leverages the strengths of
BM25 in identifying examples with terms highly similar
to the query, to select the most relevant examples for the
specific task at hand. This strategy ensures the retrieved
examples are topically relevant to the task while potentially
introducing some variation in the specific phrasing or
wording used.
          </p>
          <p>
            Finally, neural ranking, one of the most commonly used
ICL approach, typically yielding superior results [
            <xref ref-type="bibr" rid="ref15 ref16 ref17 ref18 ref19">15, 16, 17,
18, 19</xref>
            ], is maximizing similarity in a dense embeddings
space. These methods, like KATE [
            <xref ref-type="bibr" rid="ref20">20</xref>
            ], utilize  -Nearest
Neighbors (kNN) search using the cosine distance of sentence
embeddings to retrieve the examples most semantically
similar to the prompt. Scaling this method leverages vector
search algorithms, commonly used in large-scale
information retrieval tasks, where eficient retrieval of semantically
similar documents is crucial.
          </p>
          <p>
            While general purpose pre-trained embeddings like BERT
[
            <xref ref-type="bibr" rid="ref21">21</xref>
            ] form a strong baseline, learning specific embeddings
for retrieval, and in particular ICL, is a very active area of
research. In [
            <xref ref-type="bibr" rid="ref22">22</xref>
            ] the authors build upon BERT and introduce
ColBERT that improves the retrieval performances by an
order of magnitude. Other embeddings model have been
proposed for ICL retrieval in [
            <xref ref-type="bibr" rid="ref16">16</xref>
            ] and [
            <xref ref-type="bibr" rid="ref17">17</xref>
            ]. Some authors
also explored training full language models [
            <xref ref-type="bibr" rid="ref15">15</xref>
            ], as well
as LLM [
            <xref ref-type="bibr" rid="ref19">19</xref>
            ], showing further improvements compared to
traditional embedding-based approaches. While leading to
superior results, these supervised neural ranking models
for learning-to-rank necessitate orders of magnitude more
training examples data, that is typically not available to
practitioners. In addition, without any explicit metric space
such as dense embeddings, eficient retrieval indexing such
as [
            <xref ref-type="bibr" rid="ref23">23</xref>
            ] cannot be used.
          </p>
        </sec>
        <sec id="sec-2-2-3">
          <title>2.1.4. Diversity/Relevance Trade-of</title>
          <p>
            While both relevance and diversity are crucial for
efective few-shot learning, methods yielding the best ICL
results combine these two paradigms rather than prioritizing
one over the other. This is achieved by maximizing a
carefully balanced trade-of between semantic similarity to the
prompt and diversity of the retrieved examples.
Unsupervised techniques can be adapted to prioritize the selection
of examples that are both relevant to the prompt and
dissimilar to each other. In [
            <xref ref-type="bibr" rid="ref24">24</xref>
            ] the authors introduce a greedy
method to select relevant demonstrations while ensuring
enough coverage. They define specific coverage strategies
adapted to the problem of program generation. In [
            <xref ref-type="bibr" rid="ref25">25</xref>
            ] the
authors employs an active learning setting, where a voting
algorithm selects a set of examples penalizing the top-
closest from already selected ones, using cosine distance in an
embedding space.
          </p>
          <p>
            The most popular unsupervised approach for achieving
this balance between relevance and diversity is Maximal
Marginal Relevance (MMR). MMR retrieves a set of
examples by iteratively selecting the example that maximizes a
linear combination of the scores of relevance to the prompt
and dissimilarity to the previously retrieved examples. It
was analyzed in [
            <xref ref-type="bibr" rid="ref26">26</xref>
            ] for ICL and was shown to outperform
simpler methods. Alternatively to MMR, Determinantal
Point Processes (DPP) has been used in [
            <xref ref-type="bibr" rid="ref18">18</xref>
            ] to optimize
the joint information of the selected  examples. However,
exactly solving the DPP optimization being NP-hard, hence
the authors also employs greedy maximization.
          </p>
        </sec>
      </sec>
      <sec id="sec-2-3">
        <title>2.2. Diversity in Information Retrieval and</title>
      </sec>
      <sec id="sec-2-4">
        <title>Online Learning</title>
        <p>The concept of diversity in information retrieval has been a
long-running topic of research. In this section we propose a
short review of the use of diversity in the IR literature and
related domains.</p>
        <sec id="sec-2-4-1">
          <title>2.2.1. In Information Retrieval</title>
          <p>
            The MMR algorithm was analyzed in [
            <xref ref-type="bibr" rid="ref27">27</xref>
            ], and compared
against other approached like KL-divergence optimization in
[
            <xref ref-type="bibr" rid="ref28">28</xref>
            ]. Pure retrieval algorithms typically optimize for recall,
not information maximization. Agreeing on a diversity
objective function remains a challenge. Diversity is sometimes
introduced as a heuristic to cover possible interpretations of
the same query, instead of minimizing information overlap
from near-duplicated results. In [
            <xref ref-type="bibr" rid="ref10">10</xref>
            ] the authors leverage a
concept of information nuggets with documents to estimate
the redundancy of the set of retrieved documents. Topic
modeling is also employed, such as [
            <xref ref-type="bibr" rid="ref29">29</xref>
            ] that uses a
taxonomy of categories labelling the documents and the queries.
The desired properties of diverse retrieval are furthermore
characterized in [
            <xref ref-type="bibr" rid="ref30">30</xref>
            ]. A various set of similarity methods
and diversification algorithms are analyzed in [
            <xref ref-type="bibr" rid="ref31">31</xref>
            ] on sparse
features vectors. Among diversity evaluation methods based
on topic modelling, three notable criteria used in the TREC
Diversity track [
            <xref ref-type="bibr" rid="ref32">32</xref>
            ], ERR-IA [
            <xref ref-type="bibr" rid="ref33">33</xref>
            ],  -nDCG@ [
            <xref ref-type="bibr" rid="ref10">10</xref>
            ], and NRBP
[
            <xref ref-type="bibr" rid="ref34">34</xref>
            ], are compared in [
            <xref ref-type="bibr" rid="ref35">35</xref>
            ].
          </p>
        </sec>
        <sec id="sec-2-4-2">
          <title>2.2.2. In Recommender Systems</title>
          <p>
            Within IR, the recommender system literature brings an
additional point-of-view on studying diversity in retrieval,
by focusing on the benefit of diverse results for a user,
instead of evaluating methods against a potentially arbitrary
relevance/diversity trade-of. The dificulty of evaluating
the impact of diversity, and the necessity for large scale
real-world recommendation studies has been explored in
[
            <xref ref-type="bibr" rid="ref36">36</xref>
            ]. In [
            <xref ref-type="bibr" rid="ref37">37</xref>
            ] and [
            <xref ref-type="bibr" rid="ref38">38</xref>
            ] the authors model the user behavior
conditioned on the set of retrieved items. In [
            <xref ref-type="bibr" rid="ref39">39</xref>
            ] the authors
improve the diversity versus relevance trade-of in
recommender systems by directly learning a ranking model that
favor diversity, instead of only applying diversity re-ranking
methods.
          </p>
        </sec>
        <sec id="sec-2-4-3">
          <title>2.2.3. In Online Learning</title>
          <p>
            Learning a trade-of between relevancy and diversity also
naturally occurs in related online frameworks such as active
learning, multi-armed bandits and Bayesian optimization.
In [
            <xref ref-type="bibr" rid="ref40">40</xref>
            ] the authors modify a learning-to-rank algorithm
from users feedback, to inherently learn diverse rankings
and demonstrate a positive impact on the original relevance
metric. Other approaches such as [
            <xref ref-type="bibr" rid="ref41">41</xref>
            ] also introduce
diversity in learning-to-rank algorithms while preserving the
ofline settings, but then are limited to evaluate using direct
diversity measures.
          </p>
          <p>
            Within batch-mode Bayesian optimization, in [
            <xref ref-type="bibr" rid="ref42">42</xref>
            ] and
[
            <xref ref-type="bibr" rid="ref43">43</xref>
            ] the authors analyze two greedy
exploration/exploitation algorithms to select the next batch of items maximizing
the cumulative reward. Like with recommender systems,
these online settings exemplify the theoretical and empirical
importance of diversifying the selected set of items despite
the true objective function only including pure relevance,
the cumulative reward.
          </p>
        </sec>
      </sec>
      <sec id="sec-2-5">
        <title>2.3. Quality Biases in Information Retrieval</title>
        <p>Complementing the discussion on diversity in information
retrieval, quality bias also plays a crucial role in efective
retrieval. Quality bias refers to the prioritization of documents
or examples considered to be more reliable or informative
within the retrieved set. Incorporating quality
considerations into retrieval algorithms can significantly improve
standard unbiased IR metrics.</p>
        <p>Several approaches have been explored to address quality
bias in pure IR tasks. These can be broadly categorized into
content-based and graph-based methods.</p>
        <sec id="sec-2-5-1">
          <title>2.3.1. Content-Based Quality Biases</title>
          <p>
            Content-based methods leverage existing signals inside the
documents themselves to identify potentially lower-quality
content. Examples include spam detection scores developed
in works like [
            <xref ref-type="bibr" rid="ref44">44</xref>
            ] and [
            <xref ref-type="bibr" rid="ref45">45</xref>
            ]. By incorporating such scores
during retrieval, the system can prioritize higher quality
documents. More sophisticated content-based approaches don’t
limit at spam classification, but extract more generic quality
features the content of documents. Works like [
            <xref ref-type="bibr" rid="ref46">46</xref>
            ] explore
features such as stop-word statistics or entropy of the
documents to generate quality scores. The authors demonstrate
that biasing standard retrieval using these features leads
to improved retrieval efectiveness even using unbiased IR
metrics like nDCG.
          </p>
        </sec>
        <sec id="sec-2-5-2">
          <title>2.3.2. Graph-Based Quality Biases</title>
          <p>
            Instead of relying on the content itself, graph-based
algorithms inherently capture implicit quality signals within
their ranking model. PageRank, a seminal algorithm for
web search ranking introduced in [
            <xref ref-type="bibr" rid="ref47">47</xref>
            ], exemplifies this
approach. PageRank leverages the links structure between
web articles to assign higher importance to web pages that
are linked to by other high-quality pages. This process
implicitly prioritizes documents with a higher perceived
quality based on the quality of their in-links.
          </p>
        </sec>
        <sec id="sec-2-5-3">
          <title>2.3.3. Connections to Recommender Systems</title>
          <p>Interestingly, the concept of inherent quality bias in
graphbased IR approaches resembles collaborative filtering
techniques employed in recommender systems. In an analogous
manner to learning-to-rank on a (item, item) graph,
collaborative filtering addresses learning-to-rank on a bipartite
(user, item) graph. In this way, collaborative filtering also
implicitly learns a trade-of between item similarity and
popularity, favoring items that are both similar to the user’s
past preferences and also generally well-received by other
users.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>Methodology</title>
      <p>We propose to frame the ICL problem as an item-cold-start
recommendation problem, where the query is an unseen
item, and the objective is to retrieve from the pool of
candidate few-shot demonstrations a set of items maximizing
the cumulative reward to the user (the LLM). In this case,
the reward is a measure of how much the retrieved items
increase the probability that the LLM generates a correct
answer. A solution to this optimization problem requires
not only relevance, but also diversity and quality in the
retrieved items, such that the amount of useful information
presented to the LLM in the context is maximized.</p>
      <p>Further, we propose to measure the impact of diversity
on the retrieved items by directly calculating the probability
of the LLM generating a correct answer given the context
items. This is in contrast to a typical retrieval context where
the retriever is evaluated by calculating some metric
relating to the accuracy and recall of documents most similar
to the query. In such a setting, it is typical to add a term
to the metric which measures the diversity of the retrieved
documents to promote more diverse retrievers, knowing
that diversity improves the reward to the user but
without having an explicit model connecting diversity to the
user’s reward. In the case of retrieving demonstrations for
inclusion in an LLM’s context, we can directly measure the
impact of diversity on the LLM’s reward by calculating the
probability of the LLM generating a correct answer.</p>
      <sec id="sec-3-1">
        <title>3.1. Problem Statement</title>
        <p>Consider an answer  that should be generated by an LLM
in response to a query  . The query can be a simple question
such as ”Who was the first man to walk on the moon?”, or
more general message such as ”I’d like to find red shoes”.
The answer could take on many forms, such a factual
response ”Neil Armstrong”, a clarifying question ”What size
and style of shoe are you looking for?”, a JSON payload to
send to an API ”{"search_terms":["red","shoe"]}” etc.</p>
        <p>Consider a set of demonstrations  , where each
demonstration is a pair (, )
answer  , or a triple (, , )̄
containing a query  and correct</p>
        <p>which additionally contains an
incorrect answer  .̄ Datasets under this later triplet form
are commonly used in Contrastive Learning approaches.
We call  , a subset of demonstrations retrieved from  , the
context.</p>
        <p>⊂  =</p>
        <p>{(  ,   ,  ̄ ), … , (  ,   ,  ̄ )}</p>
        <p>Given an auto-regressive LLM  , the query  , and a
retrieved context  , we define   ( ∣ , )</p>
        <p>generates the answer  . In practice, the tokens of the
examples from the context  are appended to the tokens of
the query  , using prompt formatting techniques that may
the probability that
be optimized to a specific LLM.
  ( ∣ ,   ()) is maximized.</p>
        <p>Putting it all together, for an unseen query  and unseen
correct answer  , a few-shot retriever  
retrieve a subset of  demonstrations   () ∈   such that
must eficiently</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Evaluation</title>
        <p>Consider the probability of generating the correct answer
 given an empty context   ( ∣ ) . We are interested in
evaluating how much the context  increases the probability
of the correct answer  . That is, we want a metric which is
related to diference of   ( ∣ , )
and   ( ∣ ) .</p>
        <p>In a pure retrieval setting, we would be interested in
finding the context  which contains the  demonstrations that
are most similar to the  . And we could argue that if there
exists a smooth function  ∶  → 
which maps a query to
its correct answer, then by retrieving the demonstrations
whose queries are nearest to  , we should also be retrieving
the answers which are closest to  , and this should help the
language model</p>
        <p>generate the correct answer  .</p>
        <p>However, it is doubtful that the space in which  is
compared to the demonstrations is one in which the function
 ∶  →</p>
        <p>is smooth, so it is not necessarily true that
the retrieved answers are closest to  . Nor is it necessarily
true that   ( ∣ , )</p>
        <p>is maximized when  contains those
answers closest to  . Consider that the answer  might
depend on some information which isn’t contained in  or any
nearby answer.</p>
        <p>Therefore, we prefer to measure   ( ∣ , )
directly.</p>
        <p>In practice, given that</p>
        <p>is an auto-regressive language
model, this is done by taking the product of the
probability of each token generated by  . The model generates
text sequentially by predicting one token at a time based
on the previously generated tokens. Let  = ( 1,  2, … ,   )
represent a sequence of tokens produced by the model. The
probability of the model generating the sequence  can be
expressed as the joint probability of generating each token
in the sequence, conditioned on the tokens that precede it.
This can be mathematically represented as:
() = (
1) ⋅ ( 2| 1) ⋅ ( 3</p>
        <p>| 1,  2) ⋯ (  | 1,  2, … ,  −1 )
Thus,   ( ∣ , )</p>
        <p>is the product of the conditional
probabilities of each token, and these probabilities are output by
the LLM at inference time and are readily available in APIs
serving LLMs such as the OpenAI API.</p>
        <sec id="sec-3-2-1">
          <title>3.2.1. Classification Metrics</title>
          <p>In binary classification, accuracy is typically used as an
evaluation metric, and can be defined as:
1
| |
(,,)∈̄
∑
1(( ∣ ) &gt; ( ∣̄ )
)</p>
          <p>Where: | | is the number of examples in the dataset  ;
1(⋅)is the indicator function that returns 1 if the condition
is true and 0 otherwise; and  ( )̄ is the correct (incorrect)
label for example  .</p>
          <p>Given a retriever   and a demonstration (, , )̄ ∈ 
we introduce the simplified leave-one-out notation () =
() . We define the metric MC1 which is related
  ∖{(,,)}̄
to accuracy:</p>
          <p>MC1 =
1
| |</p>
          <p>∑
(,,)∈̄
1(  ( ∣ , ()
to the case that multiple correct answers a and multiple
incorrect answers ā are provided for each query. This metric
is the average number of correct answers which have greater
probability than all incorrect answers.</p>
          <p>MC2 =
1
| |</p>
          <p>∑ 1 ∑ ∏ 1(  ( ∣ , ()
(, a,ā)∈ |a| ∈ a ∈̄ ā</p>
          <p>Finally, we define the related metric MC3. This metric is
the ratio of probability of correct answers to the probability
of incorrect answers.</p>
          <p>
            These metrics and their names follow those defined in
[
            <xref ref-type="bibr" rid="ref48">48</xref>
            ]. While they are easy to interpret, these metrics are not
well normalized: they don’t take into account all possible
correct and incorrect answers. As a result, if the sample of
correct and incorrect answers have varying lengths and use
of rare vocabulary tokens, these will impact the metrics.
          </p>
        </sec>
        <sec id="sec-3-2-2">
          <title>3.2.2. Direct Preference Optimization Metric</title>
          <p>We postulate that an ideal metric should obey the following
properties: it should be positive when the retrieved context
increases the probability of a correct answer; it should be
equal in magnitude when the probability of a correct
answer halves or doubles; it should relate to the probability
of getting all correct answers such that if any one correct
answer is impossible, the metric is minimized. Moreover,
in the case that incorrect answers are provided, it should
be positive when the context  increases the probability of
correct answers more than that of incorrect answers.</p>
          <p>
            We define the DPO metric as the negative of the Direct
Preference Optimization loss [
            <xref ref-type="bibr" rid="ref49">49</xref>
            ], which satisfies these
properties:
          </p>
          <p>DPO = log  ( log   ( ∣ , ()
  ( ∣ )
) − log   ( ∣̄ , ()
  ( ∣̄ )
)
)</p>
          <p>In the case that incorrect answers are not available, the
term containing  ̄ can be omitted while preserving the
aforementioned properties.</p>
          <p>Because the metric is proportional to probability ratio
  ( ∣ , )/  ( ∣ ) rather than the absolute probability
  ( ∣ , ) , it is invariant to the number of tokens and
frequency of rare vocabulary tokens in the answer. If this
were not the case, then the score for an example would get
a positive (negative) bias if the correct (incorrect) answer is
shorter. Similarly, the score across a set of examples would
weigh examples with shorter answers more strongly.</p>
          <p>Another aspect of the DPO metric that is worth
considering is that by using this metric to optimize the retriever, we
are efectively fine-tuning a model. Consider the LLM model
  ( ∣ ) which assigns a probability of a generation  given
a prompt  . Now consider another model  ′ ( ∣  ′), where
 ′ = () . From this perspective, we can consider that  ′
is functionally the same as   but with added parameters
arising from  . And so, by finding a retriever  which
maximizes the DPO metric, we are in efect fine-tuning the model
 ′ .
This section details the core algorithm employed for
fewshot demonstration retrieval, which leverages a greedy
strategy to maximize a combination of three key scores: query
relevance, demonstration diversity, and demonstration
quality bias. The full retrieval algorithm is presented in
Algorithm 1.</p>
        </sec>
        <sec id="sec-3-2-3">
          <title>3.3.1. Query Relevance</title>
          <p>
            The relevance score between the query and each candidate
demonstration is calculated using the cosine similarity of
their respective BERT embeddings [
            <xref ref-type="bibr" rid="ref21">21</xref>
            ]. By computing the
cosine similarity between the query embedding and the
embedding of each demonstration’s query, we obtain a score
that reflects the topical similarity and semantic alignment
between the query and the candidate demonstration.
          </p>
        </sec>
        <sec id="sec-3-2-4">
          <title>3.3.2. Retrieved Demonstrations Diversity</title>
          <p>To promote diversity in the retrieved demonstrations and
avoid redundancy, we incorporate the Maximal Marginal
Relevance (MMR) algorithm. MMR iteratively selects the
items that maximizes the combined score of relevance to the
query and dissimilarity to the previously chosen items. This
ensures a balance between retrieving relevant items and
ensuring they cover a variety of information. A parameter,
  , is used to control the trade-of between relevance and
diversity. Higher values of   prioritize relevance, whereas
lower values prioritize diversity.</p>
        </sec>
        <sec id="sec-3-2-5">
          <title>3.3.3. Demonstration Quality Bias</title>
          <p>While the pre-trained BERT embeddings capture semantic
relationships, they do not inherently account for the quality
of the few-shot demonstrations. To address this, we
explicitly introduce a demonstration quality bias term related to
the popularity of an item in a training dataset. This score
is computed using the log perplexity of the demonstration
answer  , given the demonstration question  .</p>
          <p>1</p>
          <p>∑ log   (  ∣ )
||   ∈</p>
          <p>
            This can be interpreted as measuring the probability of
the correct answer  given the query  , normalized to the
length of the answer. This can also been interpreted as a
proxy for a popularity bias, akin to the number of
connections of an item in graph-based retrieval algorithms like
recommender systems. Like in the article [
            <xref ref-type="bibr" rid="ref12">12</xref>
            ], the intuition
is that the more frequently a related sequence of tokens
occurs in the pre-training dataset of the LLM, the more likely
the model will be able to extract its relevant information.
Rather than directly analyzing the massive amount of text
data (often trillions of tokens) used to pre-train the LLM,
we focus on the perplexity of the sequence. Perplexity acts
as a proxy, indicating how surprised the LLM is by the
sequence, essentially, how well it aligns with what the LLM
expects to see. A parameter   controls the trade-of
between relevance/diversity and quality bias. Lower values of
  emphasize high-quality demonstrations.
          </p>
          <p>Algorithm 1 MMR with quality bias
Require: 1 ≤  ≤  ; 0 ≤   ≤ 1; 0 ≤   ≤ 1
Require:  ∈ ℝ  ▷ query embedding
Require: ∀1 ≤  ≤  ,   ∈ ℝ ▷ example question
embedding
Require: ∀1 ≤  ≤  ,   ∈ ℝ ▷ example quality bias
 ← ‖‖ ; ∀1 ≤  ≤  ,   ← ‖  ‖
∀1 ≤  ≤  ,   ←    ⊤ + (1 −   ) 
 1 ← arg max  
for 2 ≤  ≤  do
∀1 ≤  ≤  ,   ← max1≤&lt;    ⊤
∀1 ≤  ≤  ,   ←     − (1 −   ) 
  ← arg max∉{ 1,…, −1 }  
end for</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Experiments</title>
      <sec id="sec-4-1">
        <title>4.1. Experimental Setup</title>
        <sec id="sec-4-1-1">
          <title>4.1.1. The Dataset Choice</title>
          <p>We are interested in a publicly available dataset which meets
the following criteria: it should have enough statistical
power so that we can resolve small diferences in accuracy,
ideally it will have hundreds of examples or more; it doesn’t
need to have vast amounts of data as this isn’t a typical
setting for few-shot learning, and the cost of conducting
experiments can become burdensome; it should provide
correct and incorrect answers so that we can report
classification metrics from Section 3.2.1; it should be big enough
to contain similar examples with partially redundant
information so the use of diversity can improve collective
information presented to the LLM in a context.</p>
        </sec>
        <sec id="sec-4-1-2">
          <title>4.1.2. The TruthfulQA Dataset</title>
          <p>
            We chose to conduct our experiments using the TruthfulQA
dataset [
            <xref ref-type="bibr" rid="ref48">48</xref>
            ] which meets these requirements. The dataset
contains 817 distinct examples, which yields a standard error
in the range of 1% to 2% for accuracy measures in the range
of 90% to 50%. Each example contains a single query, and
a variable number of correct and incorrect answers. And
by considering each distinct (, ) pair as a demonstration
for the purpose of building a context, the retriever is faced
with similar demonstrations as multiple (, ) pairs share
the same query (on average, the dataset contains 3.5 correct
answers for each query).
          </p>
        </sec>
        <sec id="sec-4-1-3">
          <title>4.1.3. Generating Demonstrations Pairs and Triplets</title>
          <p>
            The dataset is used in three diferent ways in this paper:
•   : this is the dataset as described in [
            <xref ref-type="bibr" rid="ref48">48</xref>
            ]. It
contains 817 examples, each of which contains a
variable number of correct and incorrect answers. The
metrics MC1, MC2 and MC3, which can accept an
arbitrary number of correct and incorrect answers
as inputs, are calculated over this dataset.
•   : this is the set of every distinct (, , )̄ triple
contained in   . It contains 12,485 such triplets.
          </p>
          <p>The DPO metric is calculated over this dataset.
•    : this is the set of every distinct (, ) pairs
contained in   . It contains 2,846 such pairs. This
is the set of demonstrations from which a context is
drawn. That is,  ⊂    .</p>
          <p>When calculating a metric score for an example (  , a , ā ),
all demonstrations with the query   are left out from the
demonstrations available for inclusion in the context. In
this manner, the correct answers a are not included in the
context when the LLM is presented with query   .</p>
        </sec>
        <sec id="sec-4-1-4">
          <title>4.1.4. The Language Models</title>
          <p>
            We conducted our experiments using four noteworthy LLMs:
the smaller base text-completion model Mistral-7B-v0.1 (7B
parameters), and the larger instruct-fine-tuned mixture of
models Mixtral-8x22B-Instruct-v0.1 (141B parameters) from
Mistral [
            <xref ref-type="bibr" rid="ref50">50</xref>
            ]; as well as a smaller chat-tuned model
Llama3-8B-chat (8B parameters) and a larger chat-tuned model
Llama-3-70B-chat (70B parameters) from Llama 1.
          </p>
          <p>All four models are open-weights LLMs, meaning their
internal parameters are publicly available for scrutiny and
potential fine-tuning. These modern models stand out for
achieving impressive performance on various tasks despite
their relatively compact size. This eficiency makes it an
attractive option for resource-constrained environments
where deploying colossal models might not be feasible.</p>
        </sec>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. Implementation Details and Ablation</title>
      </sec>
      <sec id="sec-4-3">
        <title>Study</title>
        <p>We implemented the Algorithm 1 and metrics from Section
3.2.1 in python. We computed BERT embeddings using the
package sentence_transformers 2, and implemented the
retrieval algorithms in numpy. We queried all LLM models
using the Together API 3.</p>
        <p>
          We did not perform hyper-parameter tuning, and fixed
the two parameters to   = 0.75 and   = 0.95 in all
experiments. We fixed the amount of retrieved demonstrations to
 = 6 , matching the number of few-shot examples from the
ifxed primer example from the TruthfulQA paper [
          <xref ref-type="bibr" rid="ref48">48</xref>
          ].
        </p>
        <p>
          To measure the impact of the separated components of
Algorithm 1, relevance, diversity, and bias, we implemented
variants of the retrieval algorithm using only one or two of
the three components:
• Fix: fixed primer examples [
          <xref ref-type="bibr" rid="ref48">48</xref>
          ]
• Bias: Pure quality bias [
          <xref ref-type="bibr" rid="ref12">12</xref>
          ]
• Rel: Pure semantic similarity [
          <xref ref-type="bibr" rid="ref20">20</xref>
          ] (KATE)
• Rel+Bias: Semantic similarity plus quality bias
• Rel+Div: Semantic similarity plus diversity [
          <xref ref-type="bibr" rid="ref26">26</xref>
          ]
• Rel+Bias+Div: Algorithm 1
        </p>
      </sec>
      <sec id="sec-4-4">
        <title>4.3. Main Results</title>
        <p>We present the experimental metrics for the 6 retrievers for
the 4 diferent LLMs: in Table 1 and 2 for the Mistral models,
and Table 3 and 4 for the Llama-3 models.</p>
        <p>Our evaluation relies on a combination of metrics to
assess the efectiveness of diferent retrieval strategies for ICL.
The normalized DPO metric provides the most valuable
insights for each LLM individually but cannot be directly
compared across models. The three additional classification
metrics allow for objective performance comparisons across
models. However, these metrics are susceptible to bias based
on token sequence length.
1https://llama.meta.com/llama3/
2https://sbert.net/
3https://docs.together.ai/docs/inference-python</p>
        <p>The impact of few-shot learning is best seen by comparing
the three MC metrics for Rel+Div for a smaller model against
Fix for a larger model: the smaller models (7B and 8B
parameters) enriched with ICL RAG are essentially matching or
outperforming the bigger models (141B and 70B parameters)
without ICL RAG.</p>
        <p>The results consistently demonstrate that incorporating
both relevance and diversity into the retrieval strategy leads
to superior performance across all metrics and for both
LLMs. For all models, and for all metrics, Rel+Div largely
outperforms Rel. This finding reinforces the importance of
not just retrieving relevant demonstrations but also ensuring
a diverse set that maximizes the informative value for the
LLM.</p>
        <p>Interestingly, the impact of the low perplexity bias yields
contrasting results. For both Mistral models, adding this
bias results in a decline in performance on almost all metrics.
Conversely, both Llama-3 models exhibit overall
improvement with the low perplexity bias, in particular with the
DPO metric. This intriguing observation suggests that
LLMdependent hyper-parameter tuning of   might be necessary
to optimize retrieval strategies for specific models.
Alternatively, the low perplexity bias itself may benefit from
further refinement. Using an opposite intuition, we may
argue that instead of prioritizing demonstrations the LLM
already finds likely, introducing demonstrations that
surprise the model the most could be beneficial for certain
LLMs, potentially maximizing the learning impact of each
demonstration. These findings open exciting new avenues
for future research in ICL retrieval strategies, creating a
parallel with novelty and serendipity concepts in recommender
systems.</p>
      </sec>
      <sec id="sec-4-5">
        <title>4.4. Calibrating Diversity using DPO</title>
        <p>Calibrating the amount of diversity in the retrieved set is
crucial when optimizing ICL retrieval. We highlight the
dificulty of achieving this without our proposed
methodology by demonstrating the non-monotonous relationship
between the amount of diversity in the retrieved
demonstrations and the resulting benefit to the LLM performance.
To quantify diversity, we calculate the average cosine
similarity between the BERT embeddings of each demonstration
pair within the retrieved set. The LLM’s benefit is measured
using the DPO metric. We then systematically vary   while
keeping the LLM fixed ( Llama-3-8B-chat), the quality bias
ifxed (   = 0.95), and the number of retrieved
demonstrations constant ( = 6 ) to observe the empirical correlation
between diversity and DPO. The results are visualized in
Figure 1. This experiment underscores the importance of
a metric measuring the impact of the retrieved context on
the LLM, like DPO. Without such a metric, it would be
challenging to efectively calibrate   and achieve the optimal
balance between relevance and diversity in the retrieved
demonstrations.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Discussion: Real-World RAG</title>
    </sec>
    <sec id="sec-6">
      <title>Systems</title>
      <p>While the importance of diversity in ICL retrieval is
paramount, we note that readily available RAG systems
rarely implement it directly within the core retrieval
algorithm. There are several practical considerations to keep in
mind for successful deployment.</p>
      <sec id="sec-6-1">
        <title>5.1. Balancing Performance and Eficiency</title>
        <p>
          Retrieval latency is crucial at scale. Exhaustive, brute-force
nearest neighbor search is computationally expensive and
impractical. Instead, real-world systems leverage eficient
indexing techniques and approximated kNN algorithms, as
described in [
          <xref ref-type="bibr" rid="ref23">23</xref>
          ], to ensure fast retrieval times. This
approach is essential for handling large datasets while
maintaining responsiveness. To seamlessly integrate with
existing retrieval engines and leverage their optimized search
capabilities, a retrieval algorithm for RAG must ensure its
data is stored in a format compatible with these engines.
Commonly indexed data structures include text itself or
low-dimensional dense vector embeddings. By adhering
to these indexing practices, RAG systems can efectively
leverage the power of existing retrieval engines and achieve
fast, scalable retrieval of informative examples.
        </p>
      </sec>
      <sec id="sec-6-2">
        <title>5.2. ICL RAG versus Fine-Tuning</title>
        <p>The computational cost of ICL may be evaluated against
the cost of fine-tuning. For instance, consider a large LLM
like gpt-3.5 with a current price 6x larger per input tokens
between fine-tuned or default model 4. While ICL requires
additional input tokens, it is guaranteed to ofer cost savings
compared to fine-tuning when  &lt; 6 with this model.</p>
        <p>
          An interesting contrast between ICL and fine-tuning is
highlighted in the paper [
          <xref ref-type="bibr" rid="ref51">51</xref>
          ]. The paper argues that
finetuning can be more eficient than few-shot ICL in terms of
cost and latency due to the super-linear increase in LLM
latency with growing prompt sizes. However, this latency
concern is less relevant with inference-throughput
optimized LLM systems built with large GPU clusters, such as
commonly used APIs. In these systems, the observed latency
remains independent of the prompt size. From a latency
perspective, adding ICL demonstrations can be considered free.
Additionally, the paper suggests that ICL requires scanning
through 100% of the demonstrations at query time. However
this does not hold when employing real retrieval engines
with indexing and approximate kNN, which significantly
reduce the number of examples scanned during retrieval.
        </p>
        <p>Furthermore, building a curated database of few-shot
demonstrations ofers significant advantages to
practitioners. These demonstrations are not specific to a single
LLM but can be readily utilized with any LLM
architecture. This eliminates vendor lock-in and lets practitioners
leverage the best LLM for the task at hand without
concerns about compatibility. Perhaps even more importantly,
a well-maintained database of few-shot examples
automatically benefits from the continuous advancements in LLM
technology. As newer, more powerful pre-trained LLMs
become rapidly available, existing demonstrations can be
used to enrich them quickly. This ensures applications
leverage the latest capabilities without the need to completely
re-engineer workflows. This reusability and adaptability
position our few-shot learning engine as a powerful tool
for harnessing the ever-evolving potential of LLMs to solve
real business challenges.
4In May 2024, the price of gpt-turbo-0125 is $0.5/M input tokens, $1.5/M
output tokens; and fine-tuned price of $3/M input tokens, $6/M output
tokens, $8M fine-tuning tokens
Traditional full-text search algorithms like BM25 lead to
empirically lower ICL quality. Vector stores ofer a more
suitable solution for eficient retrieval based on semantic
similarity. Numerous vendors provide vector store solutions,
and they can be broadly categorized as follows:</p>
        <p>In-Memory vector indexes, such as FAISS and nmslib,
ofer exceptional speed with minimal setup complexity, but
limited scalability for larger datasets. They may not
implement in-place addition or deletion of the indexed vectors.
Self-Hosted vector databases, such as Elasticsearch and
Postgres, provide a balance between scalability and
performance, at a much larger setup complexity. They typically
implement eficient addition and deletion of the indexed
vectors. SaaS vector stores, such as Pinecone and VertexAI,
ofer a convenient option with pre-configured infrastructure
and almost no setup complexity. We invite the reader to
consult the lists of integrated vector stores of LangChain 5
and LlamaIndex 6 for near-exhaustive lists of available tools.</p>
        <p>
          Due to the complexities of incorporating such rules
directly within retrieval indexing algorithm [
          <xref ref-type="bibr" rid="ref52">52</xref>
          ], none of the
solutions known to the authors from any of the above
category implements diversity or quality biasing of the result.
A common heuristic to mitigate this problem is to retrieve
a larger set of candidate examples (e.g., double the desired
number) and then apply diversity techniques like MMR on
the retrieved candidates as a post-processing step. Quality
biasing can be indirectly achieved by modifying the indexed
embeddings themselves. For instance, reducing the norm of
embeddings associated with low-quality content can nudge
the retrieval algorithm towards higher-quality examples.
An exact implementation in the context of cosine-similarity
or dot-product relevance is to add an additional column
storing the quality bias, and set the corresponding value to
1 in the embedding of the query.
        </p>
        <p>While vector search ofers a powerful foundation for
practical ICL retrieval, it often lacks native support for essential
considerations like diversity or quality bias. These aspects
are crucial for ensuring informative and efective retrieval
of few-shot learning examples. Existing tools for
recommendation engines, on the other hand, often excel in these
areas. Recommendation engines natively incorporate rules
that promote diversity by recommending a variety of items,
or quality bias by prioritizing most popular products.
Future research directions as well as practical systems for
ICL retrieval could explore adapting or integrating these
well-established techniques from recommender systems to
further enhance the efectiveness and sophistication of
fewshot learning through information retrieval. State-of-the-art
ICL for real-world applications can be achieved by
combining the strengths of vector search with the established
”diversity-aware” retrieval approaches from recommender
systems.</p>
      </sec>
    </sec>
    <sec id="sec-7">
      <title>6. Conclusion</title>
      <p>This paper explored the critical role of information retrieval
in ICL for few-shot learning with Large Language
Models. Our work identified key desirable properties for ICL
5https://python.langchain.com/docs/integrations/vectorstores/
6https://docs.llamaindex.ai/en/stable/module_guides/storing/vector_
stores/
retrieval systems. We demonstrated that state-of-the-art
retrieval in this domain resembles recommender systems
under the item cold-start problems. Unlike traditional
information retrieval prioritizing for exact recall, our approach
emphasizes discovery by maximizing the collective
information gain from retrieved demonstrations. This necessitates
balancing query relevance, quality scoring, and diversity
to ensure a variety of informative examples are surfaced.
Furthermore, we propose a novel evaluation method for ICL
retrieval based on the subsequent performance of the
enriched LLM on NLP tasks. This approach eliminates the need
for subjective diversity scores, a challenge in information
retrieval evaluation. Our findings demonstrate the significant
impact of diversity and quality bias in retrieving
demonstrations for ICL. By incorporating these well-established
techniques from recommender systems, we can unlock the
full potential of ICL for few-shot learning and empower
LLMs to tackle real-world tasks with limited data.</p>
    </sec>
    <sec id="sec-8">
      <title>7. Acknowledgments</title>
      <p>To Ching-Wei Chen, for finding the name RAGSys, and the
entire Crossing Minds team for their support during this
research.</p>
    </sec>
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