# tablerag_milliontoken_table_understanding_with_language_models__aa7b3644.pdf

Table RAG: Million-Token Table Understanding with Language Models

Si-An Chen1 , Lesly Miculicich2, Julian Martin Eisenschlos3, Zifeng Wang2, Zilong Wang4 , Yanfei Chen2, Yasuhisa Fujii3, Hsuan-Tien Lin1, Chen-Yu Lee2, Tomas Pﬁster2

1National Taiwan University, 2Google Cloud AI Research, 3Google Deep Mind, 4UC San Diego

Recent advancements in language models (LMs) have notably enhanced their ability to reason with tabular data, primarily through program-aided mechanisms that manipulate and analyze tables. However, these methods often require the entire table as input, leading to scalability challenges due to the positional bias or context length constraints. In response to these challenges, we introduce Table RAG, a Retrieval-Augmented Generation (RAG) framework speciﬁcally designed for LM-based table understanding. Table RAG leverages query expansion combined with schema and cell retrieval to pinpoint crucial information before providing it to the LMs. This enables more efﬁcient data encoding and precise retrieval, signiﬁcantly reducing prompt lengths and mitigating information loss. We have developed two new million-token benchmarks from the Arcade and BIRD-SQL datasets to thoroughly evaluate Table RAG s effectiveness at scale. Our results demonstrate that Table RAG s retrieval design achieves the highest retrieval quality, leading to the new state-of-the-art performance on large-scale table understanding. The implementation and dataset will be available at https://github.com/ google-research/google-research/tree/master/table_rag.

1 Introduction

Recent advancements have leveraged language models (LMs) for table understanding tasks [5]. This typically involves prompting LMs with entire tables to ensure thorough analysis [24, 3, 11, 22, 10, 29]. However, scaling to larger tables poses several challenges. First, LMs face context-length constraints; for example, a medium-sized table with 100 columns and 200 rows translates into over 40,000 tokens, surpassing the limits of popular LMs like LLa MA and the GPT series. Additionally, long contexts can degrade reasoning capabilities, a phenomenon known as the Lost-in-the-Middle [9]. Finally, computation costs and latency increase signiﬁcantly with table size. Therefore, developing a scalable solution that efﬁciently handles large tables remains a critical area of research.

Naive approaches to making large table understanding feasible, such as truncating the table or only reading the schema, often result in the loss of critical information. To address this, previous works have attempted to retrieve key rows and columns to construct a sub-table that captures essential information for answering queries [8, 17]. These methods encode entire rows and columns into sparse or dense embeddings to reduce token costs for LMs, yet they still face computational and performance challenges with extremely large tables. Encoding entire rows and columns requires processing the whole table, which is infeasible for large tables containing millions of cells. Furthermore, compressing

Work done while the author was a student researcher at Google Cloud AI Research. Correspondence to: Si-An Chen<sianchen.kevin@gmail.com>, Chen-Yu Lee<chenyulee@google.com>

38th Conference on Neural Information Processing Systems (Neur IPS 2024).

(a) Read Table (b) Read Schema

(c) Row-Column

(d) Schema-Cell Retrieval (Ours)

(e) Retrieval Performance on Arcade QA

Figure 1: Comparison between table prompting techniques for LMs. (a) - (d): Data included in the LM prompt (shaded region). (a) Read Table: The LM reads the entire table, which is often infeasible for large tables. (b) Read Schema: The LM reads only the schema, consisting of column names and data types, resulting in a loss of information from the table content. (c) Row-Column Retrieval: Rows and columns are encoded and then selected based on their similarity to the question. Only the intersection of these rows and columns is presented to the LM. It is still infeasible to encode all rows and columns for large tables. (d) Schema-Cell Retrieval (our work): Column names and cells are encoded and retrieved based on their relevance to LM-generated queries about the question. Only the retrieved schema and cells are provided to the LM, enhancing efﬁciency in both encoding and reasoning. (e) Retrieval results on the Arcade QA dataset show that Table RAG outperforms other methods in both column and cell retrieval, thereby enhancing the subsequent table reasoning process. The Read Table technique is excluded as reading entire tables is typically infeasible in this context.

long rows and columns into a ﬁxed-size embedding can obscure semantic meaning, particularly when the table contains diverse or less semantically rich content (e.g., numerical values).

In this work, we introduce, Table RAG, a scalable framework that leverages retrieval-augmented generation (RAG) for LM-based table understanding. We illustrate the key differences between prior table prompting approaches and the proposed Table RAG in Fig. 1.

Our method integrates schema retrieval and cell retrieval to extract essential information from tables, enabling a program-aided LM agent to solve queries based on the provided information. Schema retrieval allows LMs to identify crucial columns and their data types solely by column names, avoiding the need to encode entire columns. Cell retrieval enables the identiﬁcation of keywords for indexing or pinpointing columns that contain necessary but hard-to-ﬁnd information missed by schema retrieval alone. To build the database for cell retrieval, Table RAG encoded each cell independently, addressing the issue faced when encoding entire rows and columns. Furthermore, Table RAG only encodes distinct and the most frequent categorical values, reducing the encoder s token cost (as shown in Fig. 3) and operating within a user-speciﬁed budget effectively. Both retrieval processes in Table RAG are enhanced by query expansion [21] with dedicated prompts for schema retrieval and cell retrieval, ensuring thorough and relevant data extraction.

Existing Table QA benchmarks typically feature only small tables with dozens of rows and columns. To verify the scalability of Table RAG for larger tables, we build two new benchmarks sourced from the real-world Arcade [26] and BIRD-SQL [7] datasets. Additionally, to assess performance across various scales, we generated synthetic data expanding tables from the Tab Fact dataset to larger sizes, while maintaining consistent questions and key table content for evaluation. Our experimental results demonstrate that Table RAG outperforms existing table prompting methods signiﬁcantly and consumes fewer tokens across different table sizes.

Our contributions can be summarized as follows:

We conduct the ﬁrst extensive study exploring the application of LMs to large-scale, real-world tables, analyzing the scalability and limitations of existing LM-based table reasoning approaches.

We introduce two new real-world benchmarks derived from Arcade and BIRD-SQL, along with an expanded synthetic dataset from Tab Fact. These datasets include tables ranging from tens to

millions of cells (Table 7), enabling comprehensive evaluation of LM capabilities across various table scales.

We develop Table RAG, an efﬁcient framework for LM-based table understanding that demonstrates superior performance on large tables while minimizing token consumption. We conduct a detailed ablation study to validate the effectiveness of each component within Table RAG.

2 Related Work

Research in table understanding has evolved from ﬁne-tuning specialized architectures [6, 4] to leveraging LMs in few-shot setups [22, 10], capitalizing on the emerging reasoning capability of these models. To enable LMs to understanding tables, table information must be included in the prompts. Representative works like Dater [24], Binder [3] and subsequent works [22, 29, 11, 10, 28] typically require LMs to process entire tables. These methods, while effective in leveraging LMs reasoning and programming capabilities for question answering, are often not feasible for larger tables due to the context length constraints.

To address the limitations of processing full tables, two main streams have emerged: schema-based and row-column retrieval methods. Schema-based methods, such as Text2SQL [30] and more recent developments [20, 18, 13, 14], focus primarily on schema understanding to generate SQL commands. This signiﬁcantly reduces token complexity but at the cost of omitting valuable cell data. Rowcolumn retrieval methods, such as ITR [8] and TAP4LM [17], attempt to address scalability issues by encoding and retrieving essential rows and columns. While this strategy reduces input lengths for reasoning, it still requires substantial computation to encode entire rows and columns and can suffer from poorer embedding quality for long sequences.

Our approach, Table RAG, innovates by combining schema retrieval with selective cell value retrieval and frequency-aware truncation. This creates an efﬁcient table prompting method where the input length to LMs is independent of table sizes. This strategy signiﬁcantly reduces computational demands while preserving the beneﬁts of accessing table contents, leading to superior performance compared to other methods across various scales.

3 Table RAG

3.1 Motivation

An illustration of the workﬂow of our method is shown in Fig. 2. The core idea is to incorporate schema retrieval and cell retrieval to obtain necessary information for solving the questions by program-aided LMs. In practice, we often ﬁnd that processing the entire table for LMs is unnecessary. Instead, the critical information usually lies in speciﬁc column names, data types, and cell values that directly relate to the question. For example, consider the question "What is the average price for wallets?" To address this, a program may simply need to extract rows related to "wallets" and then calculate the average from the price column. Knowing just the relevant column names and how "wallets" are represented in the table sufﬁces to write the program. Our method, Table RAG, leverages the observation and addresses the context length limitations by RAG.

3.2 Problem Formulation

In large-scale table understanding, we are presented with a table T, represented as T = vij | i N, j M, where N is the number of rows, M is the number of columns, and vij is the cell value at row i and column j. We address a natural language question Q and aim to produce an answer A by an LM L. Given the often impractical size of T for direct processing, a table prompting method P is employed to transform T into a more manageable prompt P(T), allowing L to effectively generate the answer A = L(P(T)). Our objective is to develop an efﬁcient P that signiﬁcantly reduces the size of the prompt, |P(T)|, compared to the original table, |T|, making it feasible for the LM to process large tables.

3.3 Core Components of Table RAG

Tabular Query Expansion To effectively manipulate the table, it is essential to pinpoint the precise column names and cell values necessary for the query. Unlike previous works [8, 17] that may use the question as a single query, we propose generating separate queries for both schema and cell values. For instance, for a question like "What is the average price for wallets?", the LM is prompted

Schema Query 3 Schema Query 2 Cell Query 1

Schema Query 3 Schema Query 2 Schema Query 1

Cell DB (Col-Cell Pairs)

Relevant Schema & Cells

Program Aided LM

Tabular Query Expansion Schema & Cell Retrieval

Figure 2: Workﬂow of the Table RAG Framework. The table is utilized to build the schema and cell databases. A question is then expanded into multiple schema and cell queries by LMs. These queries are sequentially utilized to retrieve schemas and column-cell pairs. The top K candidates from each query are combined and fed into the LM solver s prompt to answer the question. The pseudocode and an answering example on Arcade QA can be found in Alg. 1 and Fig. 8 respectively.

to produce potential queries for column names such as "product" and "price", and for relevant cell values like "wallet". These are then used to retrieve relevant schema and cell values from the table.

Schema Retrieval Following the generation of queries, the schema retrieval fetches pertinent column names using a pre-trained encoder fenc, which encodes the queries and matches them against the encoded column names to determine relevance. The retrieved schema data includes column names, data types, and example values. We convert columns to integer, ﬂoat, or datetime data types when feasible; otherwise, we keep them as categorical columns. For columns identiﬁed as numerical or datetime data type, we display the minimum and maximum values as example values. Conversely, for categorical columns, we present the three most frequent categories as example values. We combine the top-K retrieval results for each query and rank them by their similarity to the closest query. The retrieved schema provides a structured overview of the table s format and content that will be used for more targeted data extraction.

Cell Retrieval Following schema retrieval, we proceed to extract speciﬁc cell values needed to answer the question. This involves building a database of distinct column-value pairs from T, denoted as V = S

ij(Cj, vij), where Cj is the column name of the j-th column. In practice, the set of distinct values is often much smaller than the total number of cells, as illustrated in Fig. 3. This discrepancy signiﬁcantly enhances the efﬁciency of cell retrieval.

Cell retrieval plays an crucial role in Table RAG. It enhances LM s table understanding capabilities in:

1. Cell Identiﬁcation: It allows LMs to accurately detect the presence of speciﬁc keywords within the table, which is essential for effective indexing. For example, it can distinguish between terms like tv and television , ensuring that searches and operations are based on precise data entries.

2. Cell-Column Association: It also enables LMs to associate particular cells with their relevant column names. This is crucial when questions pertain to speciﬁc attributes, such as linking the term wallet directly to the description column, thereby enables row-indexing.

It should be noted that cell retrieval is primarily beneﬁcial when indexing by cell values is required. In other scenarios, simply knowing the schema may sufﬁce. For example, to answer the question "What is the average price?", identifying the relevant column name for prices is sufﬁcient because the actual computation of the average can be handled programmatically. Nevertheless, cell retrieval still improves Table RAG with additional key values from the table, which will be shown in Sec 4.8.

Cell Retrieval with Encoding Budget In the worst case, the number of distinct values could match the total number of cells. To maintain the feasibility of Table RAG in such cases, we introduce a cell encoding budget B. If the number of distinct values exceeds B, we restrict our encoding to the B most frequently occurring pairs, thus improving efﬁciency when processing large tables. It is important to note that the encoding budget impacts only the cell retrieval process. Even if a cell is not included for retrieval, the subsequent solver can still access the cell if its column name is known

Table 1: Token complexities of primary table prompting approaches without truncation. Note that Read Schema does not aware of any cell content. N: number of rows, M: number of columns, K: number of top retrieval results, D: number of distinct values in the table. It is generally observed that K < M D NM.

Table Prompting Approach Methods Token Complexity

Dater [24] Binder [3] Multi Table QA [11] Chain-of-Table [22] Mix-SC [10] Table Llama [28] Re Ac Table [29]

Reasoning: O(NM)

Read Schema

MAC-SQL [20] SQL-Pa LM [18] DIN-SQL [13] DTS-SQL [14]

Reasoning: O(M)

Row-Col Retrieval ITR [8] TAP4LM [17] Encoding: O(NM) Reasoning: O(K2)

Schema-Cell Retrieval Table RAG (our work) Encoding: O(D) Reasoning: O(K)

Figure 3: Histogram of the proportion of number of distinct values to number of cells in Arcade QA and Bird QA. The ﬁgure indicates that for most tables, the number of distinct values (D) are much smaller than the number of cells (NM).

through schema retrieval or other cells. For instance, as shown in Fig. 8, the description column contains free-form text, which likely results in a high number of unique values, many of which may be truncated due to the cell encoding budget. Nevertheless, as long as the solver recognizes the column, it can still perform operations on that column to extract the required information.

Program-Aided Solver After obtaining the column names and cell values relevant to the question, the LMs can use these information to effectively interact with the table. Table RAG is compatible with LM agents which can interact with tables programmatically. In this work, we consider Re Act [23], which is a popular approach to extend the capability of LMs and has been used in recent literature to achieve state-of-the-art results in Table QA benchmarks [10, 29]. An example of how Table RAG works with Re Act is illustrated in Fig. 8.

3.4 Token Complexity Analysis

The efﬁciency and latency of invoking LMs are signiﬁcantly inﬂuenced by the number of input tokens. Therefore, we focus on analyzing token complexity, which refers to the complexity introduced by the number of tokens in the LM s input. We examine the token complexity of each operation within the Table RAG framework and other table prompting methods. We assume that the length of a column name, a cell value, and the question are all O(1). Note that N represents the number of rows, M represents the number of columns, D is the number of distinct text cell values, B is the cell encoding budget, and K is the number of top retrieval results.

The token complexity of primary table prompting approaches are shown in Table 1.

Read Table feeds the entire table to LMs, resulting O(NM) tokens for reasoning. Read Schema only feeds the schema to LMs, which is O(M) tokens, but loss the information from the table content. Row-Column Retrieval encodes all rows and columns to embeddings, resulting O(NM) tokens for encoding. Then it retrieves top-K rows and columns to construct a K K sub-table for reasoning, which is O(K2).

We analyze the token complexity of each step in Table RAG as follows:

Tabular Query Expansion: The prompt to the LM is primarily based on the question, which typically comprises only a few words, thus the token complexity for this component is O(1). Building Schema Database: Each column name is encoded using the encoder function fenc, resulting in a token complexity of O(M) for the encoder. Building Cell Database: This operation involves encoding distinct column-value pairs using fenc. The total number of distinct pairs D is capped at B when exceeding the limit. Therefore, the token

complexity for building the cell database is O(min(D, B)), ensuring that the most frequent data is processed to optimize performance. Note that it takes O(NM) CPU time to build the cell database, but the computation cost is negligible compared to LM calls. For example, computing the distinct values from 106 elements takes only 60 ms on a personal laptop, while it takes 1 second to encode merely hundreds of words on CPUs2.

LM Reasoning: The query expansion process generally produces approximately 3-5 queries, which are considered O(1). Each query then retrieves the top-K results, leading to a total complexity of O(K) for the columns and cell values included in the LM s prompt. This step ensures that the LM processes only the most pertinent information from the table, enhancing efﬁciency and effectiveness in generating responses.

Overall, given that typically M B and D, the token complexity for Table RAG is O(min(D, B)) for encoding and O(K) for reasoning, with neither being dependent on the overall size of the table. Consequently, Table RAG maintains manageable costs even for large tables, optimizing computational resources and response times for large-scale table understanding tasks.

4 Empirical Studies

4.1 Dataset

Existing Table QA benchmarks such as Tab Fact [2] and Wiki Table QA [12] feature small web tables that fall within the context limits of most LMs, while others like Spider dataset [27] are designed purely as text-to-SQL tasks with access only to the schema. To better assess reasoning capabilities over larger, more realistic tables, we have developed two extensive table QA datasets, Arcade QA and Bird QA, derived from the Arcade [26] and BIRD-SQL [7] datasets, respectively. Arcade QA comprises tables with an average of 79, 000 rows and a maximum of 7 million cells, while Bird QA tables feature an average of 62, 000 rows with a peak at 10 million cells. Furthermore, we expanded Tab Fact to include synthetic tables ranging from 100 100 to 1, 000 1, 000, equivalent to a million of cells, to examine the impact of different table sizes under the same question and key information. Detailed methodology for dataset generation and the statistics of these datasets are provided in Appendix C and summarized in Table 7.

4.2 Baseline

We compare Table RAG to four different approaches for incorporating table information into LMs. To ensure a fair comparison of table access strategies, we have implemented the baselines and our Table RAG based on the same Py Re Act [10, 29] solver.

Read Table This common approach in recent research includes embedding the entire table in the prompt, then asking the LMs to solve the problem with the provided table information. This approach is limited by the context length of the LMs. We discard data instances and consider them failures when the table size exceeds the context length.

Read Schema Widely-used in Text2SQL literature, this method assumes that table content is not directly accessible. It incorporates column names and data types into the prompt, enabling LMs to execute commands based on these column names without direct access to the row data.

Rand Row Sampling This method is a prevalent rule-based sampling approach [17] that randomly selects rows from the table with equal probabilities. When the total number of rows exceeds K, we select K rows to form a representative sample. This baseline is employed to underscore the beneﬁts of more targeted retrieval methods, illustrating how they can provide more relevant and efﬁcient data selection compared to random sampling.

Row Col Retrieval This state-of-the-art approach reduces table sizes prior to LM reasoning. Following the methodology of Sui et al. [17], we encode rows and columns and then retrieve the top K rows and columns based on their similarity to the question s embedding to form a sub-table. Since encoding all rows and columns requires 2NM tokens, which is impractical for large tables with millions of cells, we truncate the tables to B 2M rows. This truncation limits the number of tokens encoded to B, aligning with the token limit in our Table RAG implementation.

2https://kennethenevoldsen.github.io/scandinavian-embedding-benchmark/

Table 2: Performance comparison of table prompting approaches on Arcade QA and Bird QA across LMs.

GPT 3.5 Turbo Gemini 1.0 Pro Mistral Nemo

Method Arcade QA Bird QA Arcade QA Bird QA Arcade QA Bird QA

Read Table 4.6 9.1 1.5 4.9 5.4 8.4 Read Schema 43.1 40.3 30.8 31.8 32.3 35.7 Rand Row Sampling 42.3 34.7 20.8 25.3 28.5 33.4 Row Col Retrieval 37.7 39.6 16.9 21.8 30.0 36.4

Table RAG 49.2 45.5 42.3 44.2 46.2 45.1

Table 3: Evaluation of retrieval performance. Table RAG shows best retrieval quality on all tasks. R: recall, P: precision.

Arcade QA Bird QA

Method Column Retrieval Cell Retrieval Column Retrieval Cell Retrieval

R P F1 R P F1 R P F1 R P F1

Read Schema 100.0 12.4 23.4 0.0 0.0 0.0 100.0 30.8 41.6 0.0 0.0 0.0 Rand Row Sampling 100.0 12.4 23.4 66.5 0.5 3.5 100.0 30.8 41.6 48.9 1.7 7.2 Row Col Retrieval 99.6 12.5 23.7 62.8 0.6 5.0 93.5 31.1 42.4 52.7 4.6 14.0 Table RAG 98.3 21.2 36.6 85.4 3.4 17.6 95.3 36.0 48.8 87.4 5.7 17.3

4.3 Experimental Setup

Our experiments employ GPT-3.5-turbo [1], Gemini-1.0-Pro [19] and Mistral-Nemo-Instruct-24073 as LM solvers. In ablation study, we use GPT-3.5-turbo if not speciﬁed. We use Open AI s textembedding-3-large4 as the encoder for dense retrieval. For Table RAG, we set the cell encoding budget B = 10, 000 and the retrieval limit K = 5. For Rand Row Sampling and Row Col Retrieval, we increase the retrieval limit to K = 30. Each experiment is conducted 10 times and evaluated by majority-voting to ensure the stability and consistency. The evaluation metric is the exact-match accuracy if not speciﬁed.

4.4 Main Results

In evaluations across the datasets shown in Table 2, Table RAG consistently outperformed other methods, achieving the highest accuracies across all LMs on both Arcade QA and Bird QA. The Read Table method underperforms on both in Arcade QA and Bird QA, indicating it suffers from long context. Among the three LMs, GPT 3.5 Turbo consistently delivers the best performance, regardless of the table prompting method used. These results demonstrate the effectiveness of Table RAG in handling large-scale Table QA tasks.

4.5 Retrieval Performance Analysis

To better understand the retrieval quality of various table prompting approaches, in Table 3, we assessed the recall, precision and f1 score for the prompts fed to LMs for reasoning. The ground truths are extracted from the program annotations in the Arcade QA and Bird QA datasets. In column retrieval, while all methods achieved high recall due to the small number of columns, Table RAG demonstrated superior precision across both datasets, indicating its effectiveness in identifying the most relevant columns concisely. In contrast, Read Schema and Row Col Retrieval showed lower precision, suggesting that they retrieved more irrelevant columns. For cell retrieval, Table RAG consistently outperformed other methods on all metrics. Table RAG s high recall in cell retrieval marks a signiﬁcant improvement over other table prompting methods, indicating it can retrieve most necessary cells for the subsequent reasoning. In summary, this analysis underscores Table RAG s efﬁcacy in retrieving essential information in both the column and cell aspects.

3https://mistral.ai/news/mistral-nemo/ 4https://openai.com/index/new-embedding-models-and-api-updates/

Figure 4: Performance evaluation of Synthetic Tabfact in varying scales. Table RAG shows consistently superior results, and it decreases gracefully compared to competitive methods.

Figure 5: Impact of varying top retrieval results (K). Different K values inﬂuence both prompt length and accuracy. Each point is labeled with its corresponding K value. Table RAG retrieves the top K schema and cell values, Rand Row Sampling selects K random rows, and Row Col Retrieval retrieves K rows and K columns.

Table 4: Comparison of Table RAG with stateof-the-art methods on Wiki Table QA.

Method Accuracy

Ta BERT [25] 52.30 Text-to-SQL [15] 52.90 Binder [3] 56.74 Dater [24] 52.81

Table RAG (Ours) 57.03

Table 5: Performance comparison of different retrieval approaches in Table RAG on Arcade QA and Bird QA. Method Arcade QA Bird QA

Table RAG (BM25) 37.7 35.7 Table RAG (Hybrid) 46.2 44.5 Table RAG (Embed) 49.2 45.5

4.6 Scalability Test on Tab Fact

To understand the performance across varying table sizes under similar conditions, we create a set of synthetic data from Tab Fact with table sizes ranging from 50 50, 100 100, 500 500, and 1000 1000. The synthetic data allow us to analysis how table prompting methods perform in different scales with the same questions and key table contents. The results are shown in Fig. 4. Read Table exhibited strong initial accuracy with the original data but failed dramatically as table sizes increased, infeasible for sizes 100 and beyond due to the context length limitations. Conversely, Table RAG demonstrated the most consistent and scalable performance, decreasing moderately from 83.1 to 68.4 as table size increased to 1000 rows and columns, showcasing its effectiveness in understanding larger tables. Both Read Schema and Row Col Retrieval showed declines in performance with increasing table size, yet maintained moderate accuracy, highlighting their relative scalability compared to Read Table but less effectiveness than Table RAG in handling large tables.

4.7 Comparison with State-of-the-Art on Wiki Table QA

To evaluate performance on small-scale Table QA datasets, we compared Table RAG with state-ofthe-art approaches that rely on reading entire tables, using the commonly used Wiki Table QA [12] benchmark. As shown in Table 4, Table RAG surpasses all existing methods, including Ta BERT [25], Text-to-SQL [15], Binder [3], and Dater [24]. This highlights Table RAG s effectiveness, even in small-scale settings. These results conﬁrm that, while Table RAG is designed for large-scale Table QA, its approach is versatile and maintains state-of-the-art performance across different table sizes and complexities.

4.8 Ablation Studies

Impact of Retrieval Methods in Table RAG: Table 5 compares different retrieval approaches within Table RAG. BM25 [16], a well-known statistical retrieval method, excels in efﬁciency and can process all cells but lacks semantic understanding. We also compare it with our embedding-based retrieval and

Figure 6: Impact of cell encoding budget B. Table RAG retrieves from the B most frequent cells, maintaining robust performance even with a smaller budget. Row Col Sampling truncates more rows as B decreases, showing greater sensitivity to budget changes and generally underperforming compared to Table RAG.

Figure 7: Effect of query expansion. Query expansion consistently improves Table RAG across all scenarios, indicating that it provides better coverage of user intents.

Table 6: Ablation study of schema retrieval (Rows 1 vs 3 and 2 vs 4) and cell retrieval (Rows 1 vs 2 and 3 vs 4). The ﬁrst column indicates whether the LM processed all schemas or only retrieved schemas. The second column indicates whether the LM ignored cell values or processed retrieved column-cell pairs. Schema retrieval leads to an improvement in accuracy of up to 9.4%, while cell retrieval results in an increase of up to 11.5%.

Schema Cell GPT 3.5 Turbo Gemini 1.0 Pro

Arcade QA Bird QA Arcade QA Bird QA

all none 43.1 40.3 30.8 31.8 all retrieval 48.5 42.5 42.3 41.6 retrieval none 46.9 44.8 36.9 42.2 retrieval retrieval 49.2 45.5 42.3 44.2

a hybrid approach that combines scores from both methods. The results show that embedding-based retrieval achieves the best performance, outperforming both BM25 and the hybrid method, despite not processing the entire table due to encoding constraints. This underscores the importance of semantic understanding in retrieval, where embedding-based methods offer better comprehension of table data, signiﬁcantly enhancing Table RAG s performance.

Number of Top Retrieval Results K: Fig 5 illustrates the impact of varying the number of top retrieval results (K) on the performance and the token cost for the subsequent LM reasoning. The results demonstrate that that increasing the number K, while increasing the prompt lengths, does not consistently improve performance. Though larger K allows LMs access to more information, it also results in a longer context which can exacerbate the lost-in-the-middle phenomenon. In contrast, Table RAG excels by requiring fewer K values, thus reducing the context tokens needed and lowering subsequent reasoning costs while still outperforming other methods.

Encoding Budget B: The results from Fig. 6 demonstrate how different token encoding budgets (B) affect the performance of Table RAG and Row Col Retrieval. While a higher budget theoretically allows for more information to be retrieved, the results show that it does not always lead to better performance. Speciﬁcally, Row Col Retrieval shows a decline in performance with increased budgets, potentially due to the retrieval of more rows that complicate selecting the correct ones and produce noisier embeddings from longer column sequences. In contrast, Table RAG maintains consistent performance across various budgets, indicating that its approach of building the corpus by cell frequency effectively captures essential information even with limited budgets.

Query Expansion: The effectiveness of our query expansion method is analyzed in Fig. 7. The results demonstrate that query expansion consistently enhances Table RAG s performance across various datasets and LMs.

Schema Retrieval and Cell Retrieval: We analyze the impact of schema retrieval and cell retrieval on performance in Table 6. The results demonstrate that schema retrieval consistently enhances reasoning performance across datasets and LMs, with a maximum improvement of 9.4%, regardless of whether cell values are considered. The results indicate that even for tables with small number of columns (average 20.5 columns in Arcade QA and 11.1 columns in Bird QA), schema retrieval is still helpful to only provide relevant columns for the subsequent reasoning. Similarly, cell retrieval consistently improves accuracies across all datasets and LMs, with a maximum improvement of 11.5%, indicating cell retrieval can effectively extract key information from the table contents.

5 Conclusion

In this work, we have presented Table RAG, the ﬁrst framework to demonstrate effective and efﬁcient LM-based table understanding with millions of tokens. To ﬁll in the evaluation gap, we have introduced three new million-token scale table understanding benchmarks. Table RAG s retrieval design, combining schema and cell retrieval with frequency-aware truncation, signiﬁcantly reduces computational costs and token usage without sacriﬁcing performance. Our extensive experiments on both real-world and synthetic datasets showcase Table RAG s superior performance across various table sizes. Table RAG paves the way for future research on even larger and more complex table understanding tasks.

6 Limitations

Theoretically, the worst-case complexity for cell retrieval could reach O(NM) if all cell values are distinct, potentially leading to loss of crucial information even with frequency-based truncation. Also, our evaluation is limited to QA and veriﬁcation tasks due to the scarcity of large-scale table benchmarks. Finally, we focus on benchmarking on comparing Table RAG with other representative table prompting methods using the same LM solver, rather than against the latest state-of-the-art techniques, to speciﬁcally assess its efﬁcacy on large tables.

Acknowledgement

S.-A. Chen and H.-T. Lin are partially supported by the National Taiwan University Center for Data Intelligence via NTU-113L900901 and the Ministry of Science and Technology in Taiwan via NSTC 113-2628-E-002-003.

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[4] Julian Eisenschlos, Syrine Krichene, and Thomas Müller. Understanding tables with intermediate pre-training. In Findings of the Association for Computational Linguistics: EMNLP 2020, pages 281 296, 2020. 3

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A Table RAG Example

Schema Database

Cell Database

What is the average price for wallets?

Thought I need to filter out the prices from the given cell values.

Action df[ price ] = df['price'].str.replace('$', '').astype(float)

Observation success!

Thought Now, I need to filter out the prices for leather wallets only.

Action wallet_prices = df[df['description'] .str.contains('Wallet')][ price ]

Observation success!

Thought I should calculate the average price for wallets.

Action wallet_prices.mean()

Observation 442.7916666666667

Thought Before giving the final answer, you should think about the observations

Answer 442.7916666666667

Program-Aided LLM Solver

Name Type Example Values

price String $449 , $399 , $509

quantity Integer min: 1, max: 4

description String Lipstick , Mirror

order_date Date min: 2021-06-13 max: 2022-02-05

Relevant Information

Schema Retrieval

Column Cell Value

order_status Delivered to Buyer

description Leather Wallet with

description Clutch Purse:

description Men s Wallet with

Cell Retrieval

What is the average price for wallets?

product name, price, category

Schema Query

wallet, seller, order status

Tabular Query Expansion

Build Database

Name Type Example Values

Column Cell Value

Figure 8: Example of Table RAG in Arcade QA.

B Table RAG Pseudo Code

See Alg. 1.

Algorithm 1: Table RAG Algorithm Data: T: table, Q: questions, L: LM, K: number of retrieval results, B: token encoding budget, fenc: encoder Result: ˆA is the predicted answer to the question

1 Function Table RAG(T, Q, L, K, B, fenc):

2 schema_db Build Schema DB(T, fenc);

3 cell_db Build Cell DB(T, B, fenc);

4 foreach q Q do

5 Qschema, Qcell Tabular Query Expansion(L, q);

6 Rschema Multi Query Retrieve(fenc, Qschema, K, schema_db);

7 Rcell Multi Query Retrieve(fenc, Qcell, K, cell_db);

8 ˆA Program Aided Solver(L, q, T, Rschema, Rcell);

10 return ˆA

11 Function Build Schema DB(T, fenc):

12 corpus φ;

13 foreach (Cj, Dj, Ej) T do

14 corpus corpus (f Enc(Cj), (Cj, Dj, Ej));

16 return corpus

17 Function Build Cell DB(T, B, fenc):

18 corpus φ;

19 V get Distinct Column Cell Pairby Freq(T);

20 V V [: B];

21 foreach (Cj, vij) V do

22 corpus corpus (f Enc((Cj, vij)), (Cj, vij))

24 return corpus

25 Function Multi Query Retrieve(L, Q, K, corpus):

27 foreach q Q do

28 res res Retrieve K(q, corpus)

30 return res

Here we describe the generation of each datasets. The statistics of each dataset are shown in Table 7.

Arcade QA The ARCADE dataset [26] consists of a collection of annotated data science notebooks with natural language to code annotations for every cell. The notebooks executes on large scale Kaggle ML datasets5. We extract the examples where there is an executed result, and that result is either a single primitive value or a list of values (single column table). In contrast, examples that focus on data wrangling without a returned value, or where the result is a table are skipped. In total we obtain 130 examples with questions such as How many countries are south of the equator? and What is the city that had cash on delivery as the most common payment method? .

Bird QA We leverage a subset of BIRD dataset [7], a collection for large-scale database grounded text-to-SQL. It also contains annotations for columns descriptions, and external knowledge evidence in some examples. To convert the task to table-QA, we extract 308 examples where a single table was used. We use only the table and question without additional helper annotations such as descriptions and external knowledge evidence. The tables have 40 thousand rows in average and it comprises on single an multiple value answers.

Synthetic Tab Fact To complement existing datasets and better evaluate LMs on larger table structures, we have synthesized an extension of the Tab Fact dataset to include tables of signiﬁcantly greater sizes. This synthesis involves a series of steps designed to expand original small tables into larger ones without losing the integrity of the data or the logical consistency required for correct query answering. We utilize LM-generated column names, sampling functions, and solution programs to create tables and validate them through a rigorous process where solution programs verify the correctness of answers, ensuring the synthetic tables maintain the challenge and integrity of the original dataset.

Table 7: Dataset statistics. Values are presented in averages, except for the total counts of tables and questions.

Data # of tables # of questions # of rows (N) # of cols (M) # of cells (NM) # of distinct values (D) # of categorical columns

Arcade QA 48 130 79,376.2 20.5 1,247,946.6 50,609.4 9.4 Bird QA 53 308 62,813.1 11.1 721,077.6 39,649.5 4.9

Synth-Tab Fact-original 288 288 14.1 6.3 88.8 41.1 4.4 Synth-Tab Fact-50 288 288 50.0 50.0 2,500.0 149.1 27.0 Synth-Tab Fact-100 288 288 100.0 100.0 10,000.0 268.1 54.1 Synth-Tab Fact-500 288 288 500.0 500.0 250,000.0 1,140.5 267.2 Synth-Tab Fact-1K 288 288 1,000.0 1,000.0 1,000,000.0 2,196.8 539.9

5https://www.kaggle.com/datasets

D Prompt of Query Expansion for Schema Retrieval

========================================= Prompt =========================================

Given a large table regarding "amazon seller order status prediction orders data", I want to answer a question: "What is the average price for leather wallets?" Since I cannot view the table directly, please suggest some column names that might contain the necessary data to answer this question. Please answer with a list of column names in JSON format without any additional explanation . Example: ["column1", "column2", "column3"]

======================================= Completion ======================================= ["product_name", "category", "price"]

Figure 9: Prompt of Query Expansion for Schema Retrieval

E Prompt of Query Expansion for Cell Retrieval

========================================= Prompt =========================================

Given a large table regarding "amazon seller order status prediction orders data", I want to answer a question: "What is the average price for leather wallets?" Please extract some keywords which might appear in the table cells and help answer the question. The keywords should be categorical values rather than numerical values. The keywords should be contained in the question. Please answer with a list of keywords in JSON format without any additional explanation. Example: ["keyword1", "keyword2", "keyword3"]

======================================= Completion ======================================= ["leather wallets", "average price", "amazon seller", "order status prediction", "orders data"]

Figure 10: Prompt of Query Expansion for Cell Retrieval

F Prompt of Table RAG Solver

========================================= Prompt =========================================

You are working with a pandas dataframe regarding "amazon seller order status prediction orders data" in Python. The name of the dataframe is df . Your task is to use python_repl_ast to answer the question: "What is the average price for leather wallets?"

Tool description: - python_repl_ast : A Python interactive shell. Use this to execute python commands. Input should be a valid single line python command.

Since you cannot view the table directly, here are some schemas and cell values retrieved from the table.

Schema Retrieval Results: {"column_name": "item_total", "dtype": "object", "cell_examples": [ $449.00 , $399.00 , $549.00 ]} {"column_name": "quantity", "dtype": "int64", "min": 1, "max": 4} {"column_name": "order_no", "dtype": "object", "cell_examples": [ 402-4845680-8041921 , 405-9763961-5211537 , 404-3964908-7850720 ]} ...

Cell Retrieval Queries: leather wallets, average price, order status, prediction, amazon seller Cell Retrieval Results: {"column_name": "order_status", "cell_value": "Delivered to buyer"} {"column_name": "description", "cell_value": "Pure Leather Camel Color Gent s Wallet with Coin Compartment and Card Holders | Men s Ultra Slim Money Organiser (1 pc)"} ...

Strictly follow the given format to respond: Thought: you should always think about what to do Action: the single line Python command to execute Observation: the result of the action ... (this Thought/Action/Observation can repeat N times) Thought: before giving the final answer, you should think about the observations Final Answer: the final answer to the original input question (Answer1, Answer2, ...)

Notes: - Do not use markdown or any other formatting in your responses. - Ensure the last line is only "Final Answer: Answer1, Answer2, ..." form, no other form. - Directly output the Final Answer rather than outputting by Python. - Ensure to have a concluding thought that verifies the table, observations and the question before giving the final answer.

Now, given a table regarding "amazon seller order status prediction orders data", please use python_repl_ast with the column names and cell values above to answer the question: " What is the average price for leather wallets?"

======================================= Completion ======================================= Thought: I need to remove the comma in the item_total values before converting them to float. Action: df[ item_total ] = df[ item_total ].str.replace( $ , ).str.replace( , , ).astype( float) Observation: success! Thought: Now, I can filter out the rows with leather wallets and calculate the average price. Action: df[df[ description ].str.contains( wallet , case=False)][ item_total ].mean() Observation: 442.7916666666667 Thought: before giving the final answer, I should consider the observations and ensure that the calculations are accurate. Final Answer: The average price for leather wallets is $442.79.

Figure 11: Prompt of Table RAG solver

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Guidelines:

The answer NA means that the paper does not use existing assets. The authors should cite the original paper that produced the code package or dataset. The authors should state which version of the asset is used and, if possible, include a URL. The name of the license (e.g., CC-BY 4.0) should be included for each asset. For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided. If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset. For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.

If this information is not available online, the authors are encouraged to reach out to the asset s creators. 13. New Assets

Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets? Answer: [Yes] Justiﬁcation: Section 4, Appendix C Guidelines:

The answer NA means that the paper does not release new assets. Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc. The paper should discuss whether and how consent was obtained from people whose asset is used. At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip ﬁle. 14. Crowdsourcing and Research with Human Subjects

Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)? Answer: [NA] Justiﬁcation: The paper does not involve crowdsourcing nor research with human subjects. Guidelines:

The answer NA means that the paper does not involve crowdsourcing nor research with human subjects. Including this information in the supplemental material is ﬁne, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper. According to the Neur IPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector. 15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained? Answer: [NA] Justiﬁcation: The paper does not involve crowdsourcing nor research with human subjects. Guidelines:

The answer NA means that the paper does not involve crowdsourcing nor research with human subjects. Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper. We recognize that the procedures for this may vary signiﬁcantly between institutions and locations, and we expect authors to adhere to the Neur IPS Code of Ethics and the guidelines for their institution. For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.