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Caching Historical Embeddings in Conversational Search

11/25/2022
by   Ophir Frieder, et al.
Georgetown University
University of Pisa
Consiglio Nazionale delle Ricerche
0

Rapid response, namely low latency, is fundamental in search applications; it is particularly so in interactive search sessions, such as those encountered in conversational settings. An observation with a potential to reduce latency asserts that conversational queries exhibit a temporal locality in the lists of documents retrieved. Motivated by this observation, we propose and evaluate a client-side document embedding cache, improving the responsiveness of conversational search systems. By leveraging state-of-the-art dense retrieval models to abstract document and query semantics, we cache the embeddings of documents retrieved for a topic introduced in the conversation, as they are likely relevant to successive queries. Our document embedding cache implements an efficient metric index, answering nearest-neighbor similarity queries by estimating the approximate result sets returned. We demonstrate the efficiency achieved using our cache via reproducible experiments based on TREC CAsT datasets, achieving a hit rate of up to 75 Our achieved high cache hit rates significantly improve the responsiveness of conversational systems while likewise reducing the number of queries managed on the search back-end.

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1. Introduction

Conversational agents, fueled by language understanding advancements enabled by large contextualized language models, are drawing considerable attention (Anand et al., 2020; Zamani et al., 2022). Multi-turn conversations commence with a main topic and evolve with differing facets of the initial topic or an abrupt shift to a new focus, possibly suggested by the content of the answers returned (Mele et al., 2021; Dalton et al., 2020).

A user drives such an interactive information-discovery process by submitting a query about a topic followed by a sequence of more specific queries, possibly aimed at clarifying some aspects of the topic. Documents relevant to the first query are often relevant and helpful in answering subsequent queries. This suggests the presence of temporal locality in the lists of results retrieved by conversational systems for successive queries issued by the same user in the same conversation. In support of this claim, Figure 1 illustrates a t-SNE (van der Maaten and Hinton, 2008) bi-dimensional visualization of dense representations for the queries and the relevant documents of five manually rewritten conversations from the TREC 2019 CAsT dataset (Dalton et al., 2020). As illustrated, there is a clear spatial clustering among queries in the same conversation, as well as a clear spatial clustering of relevant documents for these queries.

We exploit locality to improve efficiency in conversational systems by caching the query results on the client side. Rather than caching pages of results answering queries likely to be resubmitted, we cache documents about a topic, believing that their content will be likewise relevant to successive queries issued by the user involved in the conversation. Topic caching is effective in Web search (Mele et al., 2020) but, as yet, was never explored in conversational search.

Topic caching effectiveness rests on topical locality. Specifically, if the variety of search domains is limited, the likelihood that past, and hence potentially cached, documents are relevant to successive searches is greater. In the Web environment, search engines respond to a wide and diverse set of queries, and yet, topic caching is still effective (Mele et al., 2020); thus, in the conversational search domain where a sequence of searches often focuses on a related if not on the same specific topic, topical caching, intuitively, should have even greater appeal than in the Web environment, motivating our exploration.

Figure 1. 2D visualization of conversational queries () and corresponding relevant documents () for 5 CAsT 2019 topics.

To capitalize on the deep semantic relationship between conversation queries and documents, we leverage recent advances in Dense Retrieval (DR) models (Xiong et al., 2021; Zhan et al., 2021; Karpukhin et al., 2020; Huang et al., 2020; Yu et al., 2021). In our DR setting, documents are represented by low-dimension learned embeddings stored for efficient access in a specialised metric index, such as that provided by the FAISS toolkit (Johnson et al., 2021). Given a query embedded in the same multi-dimensional space, online ranking is performed by means of a top- nearest neighbor similarity search based on a metric distance. In the worst-case scenario, the computational cost of the nearest neighbor search is directly proportional to the number of documents stored in the metric index. To improve end-to-end responsiveness of the system, we insert a client-side metric cache (Falchi et al., 2008, 2012) in front of the DR system aimed at reusing documents retrieved for previous queries in the same conversation. We investigate different strategies for populating the cache at cold start and updating its content as the conversation topic evolves.

Our metric cache returns an approximate result set for the current query. Using reproducible experiments based on TREC CAsT datasets, we demonstrate that our cache significantly reduces end-to-end conversational system processing times without answer quality degradation. Typically, we answer a query without accessing the document index since the cache already stores the most similar documents. More importantly, we can estimate the quality of the documents present in the cache for the current query, and based on this estimate, decide if querying the document index is potentially beneficial. Depending on the size of the cache, the hit rate measured on the CAsT conversations varies between 65% and 75%, illustrating that caching significantly expedites conversational search by drastically reducing the number of queries submitted to the document index on the back-end.

Our contributions are as follows:

  • Capitalizing on temporal locality, we propose a client-side document embedding cache for expediting conversational search systems;

  • We innovate means that assess current cache content quality necessitating document index access only needed to improve response quality;

  • Using the TREC CAsT datasets, we demonstrate responsiveness improvement without accuracy degradation.

The remainder of the paper is structured as follows: Section 2 introduces our conversational search system architecture and discusses the proposed document embedding cache and the associated update strategies. Section 3 details our research questions, introducing the experimental settings and the experimental methodology. Results of our comprehensive evaluation conducted to answer the research questions are discussed in Section 4. Section 5 contextualizes our contribution in the related work. Finally, we conclude our investigation in Section 6.

Figure 2. Architecture of a conversational search system with client-side caching.

2. A Conversational system with client-side caching

A conversational search system enriched with our client-side caching is depicted in Figure 2. We adopt a typical client-server architecture where a client supervises the conversational dialogue between a user and a search back-end running on a remote server.

We assume that the conversational back-end uses a dense retrieval model where documents and queries are both encoded with vector representations, also known as embeddings, in the same multi-dimensional latent space; the collection of document embeddings is stored, for efficient access, in a search system supporting nearest neighbor search, such as a FAISS index 

(Johnson et al., 2021). Each conversational client, possibly running on a mobile device, deals with a single user conversation at a time, and hosts a local cache aimed at reusing, for efficiency reasons, the documents previously retrieved from the back-end as a result of the previous utterances of the ongoing conversation. Reusing previously retrieved, namely cached, results eliminates the additional index access, reducing latency and resource load. Specifically, the twofold goal of the cache is: 1) to improve user-perceived responsiveness of the system by promptly answering user utterances with locally cached content; 2) to reduce the computational load on the back-end server by lowering the number of server requests as compared to an analogous solution not adopting client-side caching.

In detail, the client handles the user conversation by semantically enriching those utterances that lack context (Mele et al., 2021) and encoding the rewritten utterance in the embedding space. Online conversational search is performed in the above settings by means of top nearest neighbor queries based on a metric distance between the embedding of the utterance and those of the indexed documents. The conversational client likewise queries the local cache or the back-end for the most relevant results answering the current utterance and presents them to the requesting user. The first query of a conversation is always answered by querying the back-end index, and the results retrieved are used to populate the initially empty cache. For successive utterances of the same conversation, the decision of whether to answer by leveraging the content of the cache or querying the remote index is taken locally as explained later. We begin by introducing the notation used, continuing with a mathematical background on the metric properties of queries and documents and with a detailed specification of our client-side cache together with an update policy based on the metric properties of query and document embeddings.

2.1. Preliminaries

Each query or document is represented by a vector in , hereinafter called an embedding. Let be a collection of documents represented by the embeddings , where and is a learned representation function. Similarly, let be a query represented by the embedding in the same multi-dimensional space .

Similarity functions to compare embeddings exist including inner product (Xiong et al., 2021; Karpukhin et al., 2020; Zhan et al., 2021; Reimers and Gurevych, 2019) and euclidean norm (Khattab and Zaharia, 2020). We use STAR (Zhan et al., 2021) to encode queries and documents. Since STAR embeddings are fine-tuned for maximal inner-product search, they cannot natively exploit the plethora of efficient algorithms developed for searching in Euclidean metric spaces.

To leverage nearest neighbor search and all the efficient tools devised for it, maximum inner product similarity search between embeddings can be adapted to use the Euclidean distance. Given a query embedding and a set of document embeddings with , we apply the following transformation from to  (Neyshabur and Srebro, 2015; Bachrach et al., 2014):

(1)

where . In doing so, the maximization problem of the inner product becomes exactly equivalent to the minimization problem of the Euclidean distance . In fact, we have:

Hence, hereinafter we consider the task of online ranking with a dense retriever as a nearest neighbor search task based on the Euclidean distance among the transformed embeddings and in . Intuitively, assuming , the transformation (1) maps arbitrary query and document vectors in into unit-norm query and document vectors in , i.e., the transformed vectors are mapped on the surface of the unit sphere in .

To simplify the notation we drop the bar symbol from the embeddings and , and assume that the learned function encodes queries and documents directly in by also applying the above transformation.

2.2. Nearest neighbor queries and metric distances

Let be a metric distance function, , measuring the Euclidean distance between two embeddings in of valid documents and queries; the smaller the distance between the embeddings, the more similar the corresponding documents or queries are.

Given a query , we are interested in retrieving , i.e., the Nearest Neighbor documents to query according to the distance function . In the metric space , identifies an hyperball centered on and with radius , computed as:

(2)

The radius is thus the distance from of the least similar document among the ones in 111Without loss of generality, we assume that the least similar document is unique, and we do not have two or more documents at distance from ..

We now introduce a new query . Analogously, the set identifies the hyperball with radius centered in and including the embeddings closest to . If , the two hyperballs can be completely disjoint, or may partially overlap. We introduce the quantity:

(3)

to detect the case of a partial overlap in which the query embedding falls within the hyperball , i.e., , or, equivalently, , as illustrated222The figure approximates the metric properties in a local neighborhood of on the -dimensional unit sphere, i.e., in its locally-Euclidean -dimensional tangent plane. in Figure 3.

Figure 3. Overlapping hyperballs for and with embeddings in . Grey squares represent the embeddings of the 10 nearest neighbor documents to .

In this case, there always exists a hyperball , centered on with radius such that . As shown in the figure, some of the documents in , retrieved for query , may belong also to . Specifically, these documents are all those within the hyperball . Note that there can be other documents in whose embeddings are contained in , but if such embeddings are in , we have the guarantee that the corresponding documents are the most similar to among all the documents in  (Falchi et al., 2008). Our experiments will show that the documents relevant for successive queries in a conversation overlap significantly. To take advantage of such overlap, we now introduce a cache for storing historical embeddings that exploits the above metric properties of dense representations of queries and documents. Given the representation on the current utterance, the proposed cache aims at reusing the embeddings already retrieved for previous utterances of the same conversation for improving the responsiveness of the system. In the simplistic example depicted in Figure 4, our cache would answer query by reusing the embeddings in already retrieved for .

2.3. A metric cache for conversational search

Since several queries in a multi-turn conversation may deal with the same broad topic, documents retrieved for the starting topic of a conversation might become useful also for answering subsequent queries within the same conversation. The properties of nearest neighbor queries in metric spaces discussed in the previous subsection suggest a simple, but effective way to exploit temporal locality by means of a metric cache deployed on the client-side of a conversational DR system.

algocf[htb!]    

Our system for CAChing Historical Embeddings (CACHE) is specified in Algorithm LABEL:algo:cache. The system receives a sequence of queries belonging to a user conversation and answers them returning documents retrieved from the metric cache or the metric index containing the document embeddings of the whole collection.

When the conversation is initiated with a query , whose embedding is , the cache is empty (line 1). The main index , possibly stored on a remote back-end server, is thus queried for top documents, with cache cutoff (line 2). Those documents are then stored in the cache (line 3). The rationale of using a cache cutoff much larger than the query cutoff is that of filling the cache with documents that are likely to be relevant also for the successive queries of the conversation, i.e., possibly all the documents in the conversation clusters depicted in Figure 1. The cache cutoff relates in fact with the radius of the hyperball illustrated in Figure 3: the larger the larger and the possibility of having documents relevant to the successive queries of the conversation in the hyperball . When a new query of the same conversation arrives, we estimate the quality of the historical embeddings stored in the cache for answering it. This is accomplished by the function LowQuality( (line 1). If the results available in the cache are likely to be of low quality, we issue the query to the main index with cache cutoff and add the top results to (line 2-3). Eventually, we query the cache for the nearest neighbor documents (line 4), and return them (line 5).

Cache quality estimation

The quality of the historical embeddings stored in

for answering a new query is estimated heuristically within the function

LowQuality( called in line 1 of Algorithm LABEL:algo:cache. Given the embedding of the new query, we first identify the query embedding closest to among the ones present in , i.e.,

(4)

Once is identified, we consider the radius of the hyperball , depicted in Figure 1, and use Eq. 3 to check if falls within . If this happen, it is likely that some of the documents previously retrieved for and stored in are relevant even for . Specifically, our quality estimation heuristics considers the value introduced in Eq. 3. If , with

being a hyperparameter of the cache, we answer

with the nearest neighbor documents stored in the cache, i.e., the NN documents; otherwise, we query the main embedding index in the conversational search back-end and update the cache accordingly. This quality test has the advantage of efficiency; it simply requires computing the distances between and the embeddings of the few queries previously used to populate the cache for the current conversation, i.e., the ones that caused a cache miss and were answered by retrieving the embeddings from the back-end (lines 2 and 3 of Algorithm LABEL:algo:cache).

In addition, by changing the single hyperparameter that measures the distance of a query from the internal border of the hyperball containing the closest cached query, we can easily tune the quality-assessment heuristic for the specific needs. In the experimental section, we propose and discuss a simple but effective technique for tuning to balance the effectiveness of the results returned and the efficiency improvement introduced with caching.

3. Research questions and Experimental Settings

We now present the research questions and the experimental setup aimed at evaluating the proposed CACHE system in operational scenarios. That is, we experimentally assess both the accuracy, namely not hindering response quality, and efficiency, namely a reduction of index request time, of a conversational search system that includes CACHE. Our reference baseline is exactly the same conversational search system illustrated in Figure 2 where conversational clients always forward the queries to the back-end server managing the document embedding index.

3.1. Research Questions

Specifically, in the following we address the following research questions:

  • [align=left,leftmargin=*]

  • RQ1: Does CACHE provide effective answers to conversational utterances by reusing the embeddings retrieved for previous utterance of the same conversation?

    • How effective is the quality assessment heuristic used to decide cache updates?

    • To what extent does CACHE impact on client-server interactions?

    • How much memory CACHE requires in the worst case?

  • RQ2: How much does CACHE expedite the conversational search process?

    • What is the impact of the cache cutoff on the efficiency of the system in case of cache misses?

    • How much faster is answering a query from the cache rather than from the remote index?

3.2. Experimental settings

Our conversational search system uses STAR (Zhan et al., 2021) to encode CAsT queries and documents as embeddings with 769 dimensions333STAR encoding uses 768 values but we added one dimension to each embedding by applying the transformation in Eq. 1.. The document embeddings are stored in a dense retrieval system leveraging the FAISS library (Johnson et al., 2021) to efficiently perform similarity searches between queries and documents. The nearest neighbor search is exact, and no approximation/quantization mechanisms are deployed.

Datasets and dense representation

Our experiments are based on the resources provided by the 2019, 2020, and 2021 editions of the TREC Conversational Assistant Track (CAsT). The CAsT 2019 dataset consists of 50 human-assessed conversations, while the other two datasets include 25 conversations each, with an average of 10 turns per conversation. The CAsT 2019 and 2020 include relevance judgements at passage level, whereas for CAsT 2021 the relevance judgments are provided at the document level. The judgments, graded on a three-point scale, refer to passages of the TREC CAR (Complex Answer Retrieval), and MS-MARCO (MAchine Reading COmprehension) collections for CAsT 2019 and 2020, and to documents of MS-MARCO, KILT, Wikipedia, and Washington Post 2020 for CAsT 2021444https://www.treccast.ai/.

Regarding the dense representation of queries and passages/documents, our caching strategy is orthogonal w.r.t. the choice of the embedding. The state-of-the-art single-representation models proposed in the literature are: DPR (Karpukhin et al., 2020), ANCE (Xiong et al., 2021), and STAR (Zhan et al., 2021). The main difference among these models is how the fine-tuning of the underlying pre-trained language model, i.e., BERT, is carried out. We selected for our experiments the embeddings computed by the STAR model since it employs hard negative sampling during fine-tuning, obtaining better representations in terms of effectiveness w.r.t. ANCE and DPR. For CAsT 2019 and 2020, we generated a STAR embedding for each passage in the collections, while for CAsT 2021, we encoded each document, up to the maximum input length of 512 tokens, in a single STAR embedding.

Given our focus on the efficiency of conversational search, we strictly use manually rewritten queries, where missing keywords or mentions to previous subjects, e.g., pronouns, are resolved by human assessors.

Cache Configurations

To answer our research questions, we measure the end-to-end performance of the proposed CACHE system on the three CAsT datasets. We compare CACHE against the efficiency and effectiveness of a baseline conversational search system with no caching, always answering the conversational queries by using the FAISS index hosted by the back-end (hereinafter indicated as no-caching). The effectiveness of no-caching on the assessed conversations of the three CAsT datasets represents an upper bound for the effectiveness of our CACHE system. Analogously, we consider the no-caching baseline always retrieving documents via the back-end as a lower bound for the responsiveness of the conversational search task addressed.

We experiment with two different versions of our CACHE system:

  • a static-CACHE: a metric cache populated with the nearest documents returned by the index for the first query of each conversation and never updated for the remaining queries of the conversations;

  • a dynamic-CACHE: a metric cache updated at query processing time according to Alg. LABEL:algo:cache, where LowQuality() returns false if (see Eq. 3) for at least one of the previously cached queries, and true otherwise.

We vary the cache cutoff in and assess its impact. Additionally, since conversations are typically brief, e.g., from 6 to 13 queries for the three CAsT datasets considered, for efficiency and simplicity of design, we forgo implementing any space-freeing, eviction policy should the client-side cache reach maximum capacity. We assess experimentally that, even without eviction, the amount of memory needed by our dynamic-CACHE to store the embeddings of the documents retrieved from the FAISS index during a single conversation suffices and does not present an issue. In addition to the document embeddings, we recall that to implement the LowQuality test, our cache records also the embeddings and radius of all the previous queries of the conversation answered on the back-end.

Effectiveness Evaluation

The effectiveness of the no-caching system, the static-CACHE, and the dynamic-CACHE are assessed by using the official metrics used to evaluate CAsT conversational search systems (Dalton et al., 2020): mean average precision at query cutoff 200 (MAP@200), mean reciprocal rank at query cutoff 200 (MRR@200), normalized discounted cumulative gain at query cutoff 3 (nDCG@3), and precision at query cutoffs 1 and 3 (P@1, P@3). Our experiments report the statistically significant differences w.r.t. the baseline system for

according to the two-sample t-test.

In addition to these standard IR measures, we introduce a new metric to measure the quality of the approximate answers retrieved from the cache w.r.t. the correct results retrieved form the FAISS index. We define the coverage of a query w.r.t. a cache and a given query cutoff value , as the intersection, in terms of nearest neighbor documents, between the top elements retrieved for the cache and the exact top elements retrieved from the whole index , divided by :

(5)

where is the embedding of query . We report on the quality of the approximate answers retrieved from the cache by measuring the coverage , averaged over the different queries. The higher at a given query cutoff is, greater is the quality of the approximate nearest neighbor documents retrieved from the cache. Of course for a given cutoff and query means that we retrieve from the cache or the main index exactly the same set of answers. Moreover, these answers come out to be ranked in the same order by the distance function adopted. Besides measuring the quality of the answers retrieved from the cache vs the main index, we use the metric also to tune the hyperparameter .

To this end, Figure 4 reports the correlation between vs. cov for the CAsT 2019 train queries, using static-CACHE and . The queries with , i.e., those with no more than three documents in the intersection between the static-CACHE contents and their actual top 10 documents, correspond to . Hence, in our initial experiments, we set the value of to to obtain good coverage figures at small query cutoffs. In answering RQ1.A we will also discuss a different tuning of aimed at improving the effectiveness of dynamic-CACHE at large query cutoffs.

Figure 4. Correlation between vs. cov for the CAsT 2019 train queries, using static-CACHE, and . The vertical black dashed line corresponds to , the tuned cache update threshold value used in our experiments.
Efficiency Evaluation

The efficiency of our CACHE systems is measured in terms of: i) hit rate, i.e., the percentage of queries, over the total number of queries, answered directly by the cache without querying the dense index; ii) average query response time for our CACHE configurations and the no-caching baseline. The hit rate is measured by not considering the first query in each conversation since each conversation starts with an empty cache, and the first queries are thus compulsory cache misses, always answered by the index. Finally, the query response time, namely latency, is measured as the amount of time from when a query is submitted to the system to the time it takes for the response to get back. To better understand the impact of caching, for CACHE we measure separately the average response time for hits and misses. The efficiency evaluation is conducted on a server equipped with an Intel Xeon E5-2630 v3 CPU clocked at 2.40GHz and 192 GiB of RAM. In our tests, we employ the FAISS555https://github.com/facebookresearch/faiss Python API v1.6.4. The experiments measuring query response time are conducted by using the low-level C++ exhaustive nearest-neighbor search FAISS APIs. We perform this choice to avoid possible overheads introduced by the Python interpreter that comes into play when using the standard FAISS high-level APIs. Moreover, as FAISS is a library designed and optimized for batch retrieval, our efficiency experiments are conducted by retrieving results for a batch of queries instead of a single one. The rationale of doing this relies in the fact that, on a back-end level, we can easily assume that queries coming from different clients can be batched together before being submitted to FAISS. The reported response times are obtained as an average of three different runs.

Available Software

The source code used in our experiments is made publicly available to allow the reproducibility of the results666https://github.com/hpclab/caching-conversational-search.

4. Experimental Results

We now discuss the results of the experiments conducted to answer the research questions posed in Section 3.

max width= MAP@200 MRR@200 nDCG@3 P@1 P@3 Hit Rate CAsT 2019 no-caching 0.194 0.647 0.376 0.497 0.495 3-10 static-CACHE 1K 0.101 0.507 0.269 0.387 0.364 0.40 100% 2K 0.112 0.567 0.304 0.428 0.414 0.47 100% 5K 0.129 0.588 0.316 0.451 0.426 0.56 100% 10K 0.140 0.611 0.338 0.486 0.459 0.62 100% 3-10 dynamic-CACHE 1K 0.180 0.634 0.365 0.474 0.482 0.91 67.82% 2K 0.183 0.631 0.366 0.480 0.487 0.93 70.69% 5K 0.186 0.652 0.375 0.503 0.499 0.94 74.14% 10K 0.190 0.655 0.380 0.509 0.505 0.96 75.29% CAsT 2020 no-caching 0.212 0.622 0.338 0.471 0.473 3-10 static-CACHE 1K 0.112 0.421 0.215 0.312 0.306 0.35 100% 2K 0.120 0.454 0.236 0.351 0.324 0.41 100% 5K 0.139 0.509 0.267 0.394 0.370 0.48 100% 10K 0.146 0.518 0.270 0.394 0.380 0.52 100% 3-10 dynamic-CACHE 1K 0.204 0.624 0.339 0.481 0.478 0.91 56.02% 2K 0.203 0.625 0.336 0.481 0.470 0.93 60.73% 5K 0.208 0.622 0.341 0.476 0.479 0.94 62.83% 10K 0.210 0.625 0.339 0.476 0.476 0.96 63.87% CAsT 2021 no-caching 0.109 0.584 0.340 0.449 0.411 3-10 static-CACHE 1K 0.068 0.430 0.226 0.323 0.283 0.38 100% 2K 0.072 0.461 0.240 0.348 0.300 0.42 100% 5K 0.079 0.508 0.270 0.386 0.338 0.51 100% 10K 0.080 0.503 0.272 0.367 0.338 0.56 100% 3-10 dynamic-CACHE 1K 0.106 0.577 0.335 0.443 0.409 0.89 61.97% 2K 0.107 0.585 0.338 0.456 0.411 0.91 63.38% 5K 0.106 0.584 0.334 0.449 0.407 0.92 66.67% 10K 0.107 0.584 0.336 0.449 0.409 0.94 67.61%

Table 1. Retrieval performance measured on CAsT datasets with or without document embedding caching. We highlight with symbol statistical significant differences w.r.t. no-caching for according to the two-sample t-test. Best values for each dataset and metric are shown in bold.

4.1. RQ1: Can we provide effective cached answers?

The results of the experiments conducted on the three CAsT datasets with the no-caching baseline, static-CACHE, and dynamic-CACHE are reported in Table 1. For each dataset, the static, and dynamic versions of CACHE, we vary the value of the cache cutoff as discussed in Sec. 3.2, and highlight with symbol the statistical significant differences (two-sample t-test with ) w.r.t. the no-caching baseline. The best results for each dataset and effectiveness metric are shown in bold.

By looking at the figures in the table, we see that static-CACHE returns worse results than no-caching for all the datasets, most of the metrics, and cache cutoffs considered. However, in a few cases, the differences are not statistically significant. For example, we observe that static-CACHE on CAsT 2019 with does not statistically differ from no-caching for all metrics but MAP@200. The reuse of the embeddings retrieved for the first queries of CAsT 2019 conversations is thus so high that even the simple heuristic of statically caching the top embeddings of the first query allows to answer effectively the following queries without further interactions with the back-end. As expected, we see that by increasing the number of statically cached embeddings from to , we improve the quality for all datasets and metrics. Interestingly, we observe that static-CACHE performs relatively better at small query cutoffs since in column P@1 we have, for 5 times out of 12, results not statistically different from those of no-caching. We explain such behavior by observing again Figure 3: when an incoming query is close to a previously cached one, i.e., , it is likely that the relevant documents for present in the cache are those most similar to among all those in . The larger is query cutoff

, the lower is the probability of the least similar documents among the ones in

NN residing in the cache.

When considering dynamic-CACHE, based on the heuristic update policy discussed earlier, effectiveness improves remarkably. Independently of the dataset and the value of , we achieve performance figures that are not statistically different from those measured with no-caching for all metrics but MAP@200. Indeed, the metrics measured at small query cutoffs result in some cases to be even slightly better than those of the baseline even if the improvements are not statistically significant: since the embeddings relevant for a conversation are tightly clustered, retrieving them from the cache rather than from the whole index in some case reduces noise and provides higher accuracy. MAP@200 is the only metrics for which some configurations of dynamic-CACHE result to perform worse than no-caching. This is motivated by the tuning of threshold performed by focusing on small query cutoffs, i.e., the ones commonly considered important for conversational search tasks (Dalton et al., 2020).

RQ1.A: Effectiveness of the quality assessment heuristic

The performance exhibited by dynamic-CACHE demonstrates that the quality assessment heuristic used to determine cache updates is highly effective. To further corroborate this claim, the column of Table 1 reports for static-CACHE and dynamic-CACHE the mean coverage for measured by averaging Eq. (5) over all the conversational queries in the datasets. We recall that this measure counts the cardinality of the intersection between the top elements retrieved from the cache and the exact top elements retrieved from the whole index, divided by . While the values for static-CACHE range between 0.35 to 0.62, justifying the quality degradation captured by the metrics reported in the table, with dynamic-CACHE we measure values between 0.89 and 0.96, showing that, consistently across different datasets and cache configurations, the update heuristics proposed successfully trigger when the content of the cache needs refreshing to answer a new topic introduced in the conversation.

Figure 5. Correlation between vs. cov for the CAsT 2019 train queries, using static-CACHE and . The vertical black dashed line corresponds to , the tuned cache update threshold value used in the experiments.

To gain further insights about RQ1.A, we conducted other experiments aimed at understanding if the hyperparameter driving the dynamic-CACHE updates can be fine-tuned for a specific query cutoff. Our investigation is motivated by the MAP@200 results reported in Table 1 that are slightly lower than the baseline for out of dynamic-CACHE configurations. We ask ourselves if it is possible to tune the value of to achieve MAP@200 results statistically equivalent to those of no-caching without losing all the efficiency advantages of our client-side cache.

Similarly to Figure 4, the plot in Figure 5 shows the correlation between the value of vs. cov for the CAsT 2019 train queries with static-CACHE, and . Even at query cutoff , we observe a strong correlation between and the coverage metrics of Eq. 5: most of the train queries with coverage have a value of smaller than , with a single query for which this rule of thumb does not strictly hold. Hence, we set and we run again our experiments with dynamic-CACHE by varying the cache cutoff in . The results of these experiments, conducted with the CAsT 2019 dataset, are reported in Table 2. As we can see from the figures reported in the table, increasing from to the value of improves the quality of the results returned by the cache at large cutoffs. Now dynamic-CACHE returns results that are always, even for MAP@200, statistically equivalent to the ones retrieved from the whole index by the no-caching baseline (according to a two-sample t-test for ). The improved quality at cutoff is of course paid with a decrease in efficiency. While for (see Table 1) we measured on CAsT 2019 hit rates ranging from to , by setting we strengthen the constraint on cache content quality and correspondingly increase the number of cache updates performed. Consequently, the hit rate now ranges from to , witnessing a likewise strong efficiency boost with respect to the no-caching baseline.

max width= MAP@200 MRR@200 nDCG@3 P@1 P@3 Hit Rate no-caching 0.194 0.647 0.376 0.497 0.495 2-9 dynamic-CACHE 1K 0.193 0.645 0.374 0.497 0.491 0.83 46.55% 2K 0.193 0.644 0.375 0.497 0.493 0.91 51.15% 5K 0.194 0.645 0.375 0.497 0.493 0.93 54.02% 10K 0.194 0.648 0.375 0.497 0.493 0.94 58.05%

Table 2. Retrieval performance on CAsT 2019 of the no-caching baseline and dynamic-CACHE with .
RQ1.B: Impact of Cache on client-server interactions

The last column of Table 1 reports the cache hit rate, i.e., the percentage of conversational queries over the total answered with the cached embeddings without interacting with the conversational search back-end. Of course, static-CACHE results in a trivial 100% hit rate since all the queries in a conversation are answered with the embeddings initially retrieved for answering the first query. The lowest possible workload on the back-end is however paid with a significant performance drop with respect to the no-caching baseline. With dynamic-CACHE, instead, we achieve high hit rates with the optimal answer quality discussed earlier. As expected, the greater the value of , the larger the number of cached embeddings and the higher the hit rate. With , hit rates range between to , meaning that even with the lowest cache cutoff experimented more than half of the conversation queries in the 3 datasets are answered directly by the cache, without forwarding the query to the back-end. For , the hit rate value is in the interval , with more than of the queries in the CAsT 2019 dataset answered directly by the cache. If we consider the hit rate as a measure correlated to the amount of temporal locality present in the CAsT conversations, we highlight the highest locality present in the 2019 dataset: on this dataset dynamic-CACHE with achieves a hit rate higher that the ones measured for configurations on CAsT 2020 and 2021.

RQ1.C: Worst-case Cache memory requirements

The memory occupancy of static-CACHE is limited, fixed and known in advance. The worst-case amount of memory required by dynamic-CACHE depends instead on the value of and on the number of cache updates performed during a conversation. The parameter establishes the number of embeddings added to the cache after every cache miss. Limiting the value of can be necessary to respect memory constraints on the client hosting the cache. Anyway, the larger is, the greater the performance of dynamic-CACHE thanks to the increased likelihood that upcoming queries in the conversation will be answered directly, without querying the back-end index. In our experiments, we varied in always obtaining optimal retrieval performances thanks to the effectiveness and robustness of the cache-update heuristic.

Regarding the number of cache updates performed, we consider as exemplary cases the most difficult conversations for our caching strategy in the three CAsT datasets, namely topic 77, topic 104, and topic 117 for CAsT 2019, 2020, and 2021, respectively. These conversations require the highest number of cache updates: 6, 7, 6 for and 5, 6, 5 for , respectively. Consider topic 104 of CAsT 2020, the toughest conversation for the memory requirements of dynamic-CACHE. At its maximum occupancy, after the last cache update, dynamic-CACHE system stores at most embeddings for and embeddings for . In fact, at a given time, dynamic-CACHE stores the embedding retrieved for the first query in the conversation plus new embeddings for every cache update performed. Indeed, the total number is lower due to the presence of embeddings retrieved multiple times from the index on the back-end. The actual number of cache embeddings for the case considered is and for and , respectively. Since each embedding is represented with floating point values, the maximum memory occupation for our largest cache is bytes MB. Note that if we consider the case dynamic-CACHE, , achieving the same optimal performance of dynamic-CACHE, on CAsT 2020 topic 104, the maximum occupancy of the cache decreases dramatically to about MB.

4.2. RQ2: How much does Cache expedite the conversational search process?

We now answer RQ2 by assessing the efficiency of the conversational search process in presence of cache misses (RQ2.A) or cache hits (RQ2.B).

RQ2.A: What is the impact of the cache cutoff on the efficiency of the system in case of cache misses?

We first conduct experiments to understand the impact of on the latency of nearest-neighbor queries performed on the remote back-end. To this end, we do not consider the costs of client-server communications, but only the retrieval time measured for answering a query on the remote index. Our aim is understanding if the value of impacts significantly or not the retrieval cost. In fact, when we answer the first query in the conversation or dynamic-CACHE performs an update of the cache in case of a miss (lines 1-3 of Algorithm LABEL:algo:cache), we retrieve from the remote index a large set of embeddings to increase the likelihood of storing in the cache documents relevant for successive queries. However, the query cutoff commonly used for answering conversational queries is very small, e.g., , and . Our caching approach can improve efficiency only if the cost of retrieving from the remote index embeddings is comparable to that of retrieving a much smaller set of elements. Otherwise, even if we reduce remarkably the number of accesses to the back-end, every retrieval of a large number of results for filling or updating the cache would jeopardize its efficiency benefits.

We conduct the experiment on the CAsT 2020 dataset by reporting the average latency (in msec.) of performing NN queries on the remote index. Due to the peculiarities of the FAISS library implementation previously discussed, the response time is measured by retrieving the top- results for a batch of queries, i.e., the CAsT 2020 test utterances, and by averaging the total response time (Table 3). Experimental results show that the back-end query response time is approximately second and is almost not affected by the value of . This is expected as exhaustive nearest-neighbor search requires the computation of the distances from the query of all indexed documents, plus the negligible cost of maintaining the top- closest documents in a min-heap. The result thus confirms that large values do not jeopardize the efficiency of the whole system when cache misses occur.

2-5 1K 2K 5K 10K
no-caching 1,060 1,058 1,061 1,073
static-CACHE 0.14 0.30 0.78 1.59
dynamic-CACHE 0.36 0.70 1.73 3.48
Table 3. Average response time (msec.) for querying the FAISS back-end (no-caching) or the static-CACHE and dynamic-CACHE in case of cache hit.
RQ2.B: How much faster is answering a query from the local cache rather than from the remote index?

The second experiment conducted aims at measuring the average retrieval time for querying the client-side cache (line 4 of Algorithm LABEL:algo:cache) in case of hit. We run the experiment for the two caches proposed, i.e., static-CACHE and dynamic-CACHE. While the first one stores a fixed number of documents, the latter employs cache updates that add document embeddings to the cache during the conversation. We report, in the last two rows of Table 3, the average response time of top-3 nearest-neighbor queries resulting in cache hits for different configurations of static-CACHE and dynamic-CACHE. As before, latencies are measured on batches of queries, i.e., the CAsT 2020 test utterances, by averaging the total response time. The results of the experiment show that, in case of a hit, querying the cache requires on average less than 4 milliseconds, more than 250 times less than querying the back-end. We observe that, as expected, hit time increases linearly with the size of the static-CACHE. We also note that dynamic-CACHE shows slightly higher latency than static-CACHE. This is due to the updates of the cache performed during the conversation that add embeddings to the cache. This result shows that the use of a cache in conversational search allows to achieve a speedup of up to four orders of magnitude, i.e., from seconds to few tenths of milliseconds, between querying a remote index and a local cache.

We can now finally answer RQ2, how much does CACHE expedite the conversational search process, by computing the average overall speedup achieved by our caching techniques on an entire conversation. Assuming that the average conversation is composed of utterances, the no-caching baseline that always queries the back-end leads to a total response time of about seconds. Instead, with static-CACHE we perform only one retrieval from the remote index for the first utterance while the remaining queries are resolved by the cache. Assuming the use of static-CACHE with 10K embeddings, i.e., the one with higher latency, the total response time for the whole conversation is seconds, with an overall speedup of about over no-caching. Finally, the use of dynamic-CACHE implies possible cache updates that may increase the number of queries answered using the remote index. In detail, dynamic-CACHE with 10K embeddings obtains a hit rate of about % on CAsT 2020 (see Table 1). This means that, on average, we forward queries to the back-end that cost in total seconds. The remaining cost comes from cache hits. Hits are on average and require seconds accounting for a total response time for the whole conversation of seconds. This leads to a speedup of with respect to the no-caching solution.

The above figures confirm the feasibility and the computational performance advantages of our client-server solution for caching historical embeddings for conversational search.

5. Related Work

Our contribution relates to two main research areas. The first, attracting recently significant interest, is Conversational Search. Specifically, our work focuses on the ability of neural retrieval models to capture the semantic relationship between conversation utterances and documents, and, more centrally, with efficiency aspects of neural search. The second related area is Similarity Caching

that was initially investigated in the field of content-based image retrieval and contextual advertisement.

Neural approaches for conversational search

Conversational search focuses on retrieving relevant documents from a collection to fulfill user information needs expressed in a dialogue, i.e., sequences of natural-language utterances expressed in oral or written form (Gao et al., 2022; Zhang et al., 2018). Given the nature of speech, these queries often lack context and are grammatically poorly formed, complicating their processing. To address these issues, it is natural to exploit past queries and their system response, if available, in a given conversation to build up a context history, and use this history to enrich the semantic contents of the current query. The context history is typically used to rewrite the query in a self-contained, decontextualized query, suitable for ad-hoc document retrieval (Lin et al., 2021; Mele et al., 2021; Yang et al., 2019; Voskarides et al., 2020; Li et al., 2022). Lin et al. propose two conversational query reformulation methods based on the combination of term importance estimation and neural query rewriting (Lin et al., 2021). For the latter, authors reformulate conversational queries into natural and human-understandable queries with a pretrained sequence-to-sequence model. They also use reciprocal rank fusion to combine the two approaches yielding state-of-the-art retrieval effectiveness in terms of NDCG@3 compared to the best submission of Text REtrieval Conference (TREC) Conversational Assistant Track (CAsT) 2019. Similarly, Voskarides et al. focus on multi-turn passage retrieval by proposing QuReTeC (Query Resolution by Term Classification), a neural query resolution model based on bidirectional transformers and a distant supervision method to automatically generate training data by using query-passage relevance labels (Voskarides et al., 2020). Authors incorporate QuReTeC in a multi-turn, multi-stage passage retrieval architecture and show its effectiveness on the TREC CAsT dataset.

Others approach the problem by leveraging pre-trained generative language model to directly generate the reformulated queries (Liu et al., 2021; Vakulenko et al., 2021; Yu et al., 2020). Some other studies combine approaches based on term selection strategies and query generation methods (Kumar and Callan, 2020; Lin et al., 2021). Xu et al. propose to track the context history on a different level, i.e., by exploiting user-level historical conversations (Xu et al., 2020)

. They build a structured per-user memory knowledge graph to represent users’ past interactions and manage current queries. The knowledge graph is dynamically updated and complemented with a reasoning model that predicts optimal dialog policies to be used to build the personalized answers.

Pre-trained language models, such as BERT (Devlin et al., 2019), learn semantic representations called embeddings from the contexts of words and, therefore, better capture the relevance of a document w.r.t. a query, with substantial improvements over the classical approach in the ranking and re-ranking of documents (Lin et al., 2020). Recently, several efforts exploited pre-trained language models to represent queries and documents in the same dense latent vector space, and then used inner product to compute the relevance score of a document w.r.t. a query.

In conversational search, the representation of a query can be computed in two different ways. In one case, a stand-alone contextual query understanding module reformulates the user query into a rewritten query , exploiting the context history  (Gao et al., 2022), and then a query embedding is computed. In the other case, the learned representation function is trained to receive as input the query together with its context history , and to generate a query embedding  (Qu et al., 2020). In both cases, dense retrieval methods are used to compute the query-document similarity, by deploying efficient nearest neighbor techniques over specialised indexes, such as those provided by the FAISS toolkit (Johnson et al., 2021).

Similarity caching

Similarity caching is a variant of classical exact caching in which the cache can return items that are similar, but not necessarily identical, to those queried. Similarity caching was first introduced by Falchi et al., where the authors proposed two caching algorithms possibly returning approximate result sets for k-NN similarity queries (Falchi et al., 2008). The two caching algorithms differ in the strategies adopted for building the approximate result set and deciding its quality based on the properties of metric spaces discussed in Section 2. The authors focused on large-scale content-based image retrieval and conducted tests on a collection of one million images observing a significant reduction in average response time. Specifically, with a cache storing at most 5% of the total dataset, they achieved hit rates exceeding 20%. In successive works, the same authors analyzed the impact of similarity caching on the retrieval from larger collections with real user queries (Falchi et al., 2009, 2012). Chierichetti et al. propose a similar caching solution that is used to efficiently identify advertisement candidates on the basis of those retrieved for similar past queries (Chierichetti et al., 2009). Finally, Neglia et al. propose an interesting theoretical study of similarity caching in the offline, adversarial, and stochastic settings (Neglia et al., 2022), aimed at understanding how to compute the expected cost of a given similarity caching policy.

We capitalize on these seminal works by exploiting the properties of similarity caching in metric spaces for a completely different scenario, i.e., dense retrievers for conversational search. Differently from image and advertisement retrieval, our use case is characterized by the similarity among successive queries in a conversation, enabling a novel solution based on integrating a small similarity cache in the conversational client. Our client-side similarity cache answers most of the queries in a conversation without querying the main index hosted remotely. A similar work to our own is the one by Sermpezis et al., where authors propose a similarity-based system for recommending alternative cached content to a user when their exact request cannot be satisfied by the local cache (Sermpezis et al., 2018). The contribution is related because it proposes a client-side cache where similar content is looked for, although their focus is on how statically fill the local caches on the basis of user profiles and content popularity.

6. Conclusion

We introduced a client-side, document-embedding cache for expediting conversational search systems. Although caching is extensively used in search, we take a closer look at how it can be effectively and efficiently exploited in a novel and challenging setting: a client-server conversational architecture exploiting state-of-the-art dense retrieval models and a novel metric cache hosted on the client-side.

Given the high temporal locality of the embeddings retrieved for answering utterances in a conversation, a cache can provide a great advantage to expedite conversational systems. We initially prove that both queries and documents in a conversation lie close together in the embedding space and that given this specific interaction and query properties, we can exploit the metric properties of distance computations in a dense retrieval context.

We propose two types of caching and compare the results in terms of both effectiveness and efficiency with respect to a no-caching baseline using the same back-end search solution. The first is a static-CACHE which populates the cache with documents retrieved based on the first query of a conversation only. The second, dynamic-CACHE, proposes also an update mechanism that comes in place when we determine, via a precise and efficient heuristic strategy, that the current contents of the cache might not provide relevant results.

The results of extensive and reproducible experiments conducted on CAsT datasets show that dynamic-CACHE achieves hit rates up to 75% with answers quality statistically equivalent to that of the no-caching baseline. In terms of efficiency, the response time varies with the size of the cache, nevertheless queries resulting in cache hit are three orders of magnitude faster than those processed on the back-end (accessed only for cache misses by dynamic-CACHE and for all queries by the no-caching baseline).

We conclude that our CACHE solution for conversational search is a viable and effective solution, also opening the door for significant further investigation. Its client-side organization permits, for example, to effectively integrate models of user-level contextual knowledge. Equally interesting is the investigation of user-level, personalized query rewriting strategies and neural representations.

Acknowledgements.
This work is supported by the European Union – Horizon 2020 Program under the scheme “INFRAIA-01-2018-2019 – Integrating Activities for Advanced Communities”, Grant Agreement n.871042, “SoBigData++: European Integrated Infrastructure for Social Mining and Big Data Analytics” (http://www.sobigdata.eu).

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