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+# TransTab: Learning Transferable Tabular Transformers Across Tables
+
+Zifeng Wang1 and Jimeng $\mathbf { S u n ^ { 1 , 2 } }$   
+1 Department of Computer Science, University of Illinois Urbana-Champaign   
+2 Carle Illinois College of Medicine, University of Illinois Urbana-Champaign {zifengw2,jimeng}@illinois.edu
+
+# Abstract
+
+Tabular data (or tables) are the most widely used data format in machine learning (ML). However, ML models often assume the table structure keeps fixed in training and testing. Before ML modeling, heavy data cleaning is required to merge disparate tables with different columns. This preprocessing often incurs significant data waste (e.g., removing unmatched columns and samples). How to learn ML models from multiple tables with partially overlapping columns? How to incrementally update ML models as more columns become available over time? Can we leverage model pretraining on multiple distinct tables? How to train an ML model which can predict on an unseen table?
+
+To answer all those questions, we propose to relax fixed table structures by introducing a Transferable Tabular Transformer (TransTab) for tables. The goal of TransTab is to convert each sample (a row in the table) to a generalizable embedding vector, and then apply stacked transformers for feature encoding. One methodology insight is combining column description and table cells as the raw input to a gated transformer model. The other insight is to introduce supervised and self-supervised pretraining to improve model performance. We compare TransTab with multiple baseline methods on diverse benchmark datasets and five oncology clinical trial datasets. Overall, TransTab ranks 1.00, 1.00, 1.78 out of 12 methods in supervised learning, feature incremental learning, and transfer learning scenarios, respectively; and the proposed pretraining leads to $2 . 3 \%$ AUC lift on average over the supervised learning.
+
+# 1 Introduction
+
+Tabular data are ubiquitous in healthcare, engineering, advertising, and finance [1, 2, 3, 4]. They are often stored in a relational database as tables or spreadsheets. Table rows represent the data samples, and columns represent the feature variables of diverse data types (e.g., categorical, numerical, binary, and textual). Recent works enhance tabular ML modeling using deep networks [5, 6, 7, 8] or designing self-supervision [2, 9, 10, 11]. Those existing works require the same table structure in training and testing data. However, there can be multiple tables sharing partially overlapped columns in the real world. Hence, learning across tables is inapplicable. The traditional remedy is to perform data cleaning by removing non-overlapping columns and mismatched samples before training any ML models, which waste data resources [12, 13, 14]. Therefore, learning across tables with disparate columns and transferring knowledge across tables are crucial to extending the success of deep learning/pretraining to the tabular domain.
+
+Tables are highly structured yet flexible. The first step to achieve learning across tables is to rethink the basic elements in tabular data modeling. In computer vision, the basic elements are pixels [15] or patches, [16, 17]; in natural language processing (NLP), the basic elements are words [18] or tokens [19, 20]. In the tabular domain, it is natural to treat cells in each column as independent elements. Columns are mapped to unique indexes then models take the cell values for training and inference. The premise of this modeling formulation is to keep the same column structure in all the tables. But tables often have divergent protocols where the nomenclatures of columns and cells differ. By contrast, our proposed work contextualizes the columns and cells. For example, previous methods represent a cell valued man under the column gender by 0 referring to the codebook $\mathbf { \bar { \{ m a n : 0 , w o m a n : 1 \} } }$ . Our model converts the tabular input into a sequence input (e.g., gender is man), which can be modeled with downstream sequence models. We argue such featurizing protocol is generalizable across tables, thus enabling models to apply to different tables.
+
+![](images/94370f31a56015ca1ba3db4876b8cebf454e8075065c1dee5e6f0926c6c4024f.jpg)  
+Figure 1: The demonstration of ML modeling on different tabular data settings. Previous tabular methods only do vanilla supervised training or pretraining on the same table due to they only accept fixed-column tables. By contrast, TransTab covers more new tasks (1) to (4) as it accepts variablecolumn tables. Details are presented in $\ S$ .
+
+In a nutshell, we propose Transferable Transformers for Tabular analysis (TransTab), a versatile tabular learning framework 1. TransTab applies to multiple use cases as shown in Fig. 1. The key contributions behind TransTab are
+
+• A systematic featurizing pipeline considering both column and cell semantics which is shared as the fundamental protocol across tables.   
+• Vertical-Partition Contrastive Learning (VPCL) that enables pretraining on multiple tables and also allows finetuning on target datasets.
+
+As shown by Fig. 1, due to the fixed-column assumption, all existing works only handle supervised learning or pretraining on the same-structure tables. On the contrary, TransTab relaxes this assumption and applies to four additional scenarios, which we will elaborate on in $\ S 2 . 1$ .
+
+# 2 Method
+
+In this section, we present the details of TransTab. Fig. 2 illustrates its workflow including the following key components: 1) The input processor featurizes and embeds arbitrary tabular inputs to token-level embeddings; 2) The stacked gated transformer layers further encode the token-level embeddings; 3) Finally, the learning module includes a classifier trained on labeled data and a projector for contrastive learning. Next we will present the details of each component.
+
+![](images/2360345762e6c294b96a93e4f1190d24972776eeff0bcde0aff58b8ece6f1627.jpg)  
+Figure 2: The demonstration of TransTab framework. the input processor encodes the sample into the token-level embedding $\mathbf { E }$ ; the [cls] embedding $\mathbf { z } ^ { [ c l s ] }$ in the representation $\mathbf { Z } ^ { L }$ after $L$ gated transformer layers is used for prediction and learning. In supervised learning, $\mathbf { z } ^ { [ c l s ] }$ is leveraged by a classifier to make predictions of target $y$ ; in contrastive learning, the projected $\hat { \mathbf { z } } ^ { [ c l s ] }$ is is used for self or supervised contrastive loss.
+
+# 2.1 Application scenarios of TransTab
+
+Before presenting our method in details, we first introduce four novel applications scenarios which are tractable by TransTab, as shown in Fig. 1. Suppose we aim to predict the treatment efficacy for breast cancer trials using multiple clinical trial tables, here are several scenarios we often encounter.
+
+S(1) Transfer learning. We collect data tables from multiple cancer trials for testing the efficacy of the same drug on different patients. These tables were designed independently with overlapping columns. How do we learn ML models for one trial by leveraging tables from all trials?
+
+S(2) Incremental learning. Additional columns might be added over time. For example, additional features are collected across different trial phases. How do we update the ML models using tables from all trial phases?
+
+S(3) Pretraining+Finetuning. The trial outcome label (e.g., mortality) might not be always available from all table sources. Can we benefit pretraining on those tables without labels? How do we finetune the model on the target table with labels?
+
+S(4) Zero-shot inference. We model the drug efficacy based on our trial records. The next step is to conduct inference with the model to find patients that can benefit from the drug. However, patient tables do not share the same columns as trial tables so direct inference is not possible.
+
+Overall, we witness that the assumption of fixed table structure is the obstacle to use ML for various applications. Next we will present TransTab and demonstrate how it addresses these scenarios.
+
+# 2.2 Input processor for columns and cells
+
+We build the input processor (1) to accept variable-column tables (2) to retain knowledge across tabular datasets. The idea is to convert tabular data (cells in columns) into a sequence of semantically encoded tokens. We utilize the following observation to create the sequence: the column description (e.g., column name) decides the meaning of cells in that column. For example, if a cell in column smoking history has value 1, it indicates the individual has a smoking history. Similarly, cell value 60 in column weight indicates $6 0 \mathrm { k g }$ in weight instead of 60 years old. Motivated by the discussion, we propose to include column names into the tabular modeling. As a result, TransTab treats any tabular data as the composition of three elements: text (for categorical & textual cells and column names), continuous values (for numerical cells), and boolean values (for binary cells) . Fig. 2 illustrates a visual example of how these elements are leveraged to process the four basic types of features: categorical/textual cat, binary bin, and numerical num.
+
+Categorical/Textual feature. A category or textual feature contains a sequence of text tokens. For the categorical feature cat, we concatenate the column name with the feature value $x _ { c }$ , which forms as a sequence of tokens. This sentence is then tokenized and matched to the token embedding matrix to generate the feature embedding $\mathbf { E } _ { c } \in \mathbb { R } ^ { n _ { c } \times d }$ where $d$ is the embedding dimension and $n _ { c }$ is the number of tokens.
+
+Binary feature. The binary feature bin is usually an assertive description and its value $x _ { b } \in \{ 0 , 1 \}$ . If $x _ { b } = 1$ , then bin is tokenized and encoded to the embeddings $\mathbf { E } _ { b } \in \mathbb { R } ^ { n _ { b } \times d }$ ; if not, it will not be processed to the subsequent steps. This design significantly reduces the computational and memory cost when the inputs have high-dimensional and sparse one-hot features.
+
+Numerical feature. We do not concatenate column names and values for numerical feature because the tokenization-embedding paradigm was notoriously known to be bad at discriminating numbers [21]. Instead, we process them separately. num is encoded as same as cat and bin to get $\mathbf { E } _ { u , c o l } \in$ $\mathbb { R } ^ { n _ { u } \times d }$ . We then multiply the numerical features with the column embedding to yield the numerical embedding as $\mathbf { E } _ { u } = x _ { u } ^ { \top } \times \mathbf { E } _ { u , c o l } { } ^ { 2 }$ , which we identify gets an edge on more complicated numerical embedding techniques empirically.
+
+At last, $\mathbf { E } _ { c }$ , $\mathbf { E } _ { u }$ , $\mathbf { E } _ { b }$ all pass the layer normalization [22] and the same linear layer to be aligned to the same space, then are concatenated with [cls] embedding to yield $\mathbf { E } = \tilde { \mathbf { E } } _ { c } \otimes \tilde { \mathbf { E } } _ { u } \otimes \tilde { \mathbf { E } } _ { b } \otimes \mathbf { e } ^ { [ c l s ] }$ .
+
+As a result, all cell values are contextualized regarding the corresponding column properties thus the semantic meaning of one element can vary depending on the context composition. This formulation benefits the knowledge transfer across tables a lot. For example, previously smoked depicts the same thing as smoking history. Previous methods never capture this connection while it is possible for TransTab to learn to recognize that 1 under both columns are equivalent.
+
+# 2.3 Gated transformers
+
+The gated tabular transformer is an adaption of the classical transformer in NLP [23]. It consists of two main components: multi-head self-attention layer and gated feedforward layers. The input representation $\mathbf { Z } ^ { l }$ at the $l$ -th layer is first adopted for exploring interactions between features:
+
+$$
+\begin{array} { r } { \mathbf { Z } _ { \mathrm { a t t } } ^ { l } = \mathbb { M } \mathrm { u } \mathrm { 1 t i } \mathrm { H e a d } \mathrm { A t t n } ( \mathbf { Z } ^ { l } ) = [ \mathrm { h e a d } _ { 1 } , \mathrm { h e a d } _ { 2 } , \dots , \mathrm { h e a d } _ { h } ] \mathbf { W } ^ { O } , } \\ { \mathrm { h e a d } _ { i } = \mathrm { A t t e n t i o n } ( \mathbf { Z } ^ { l } \mathbf { W } _ { i } ^ { Q } , \mathbf { Z } ^ { l } \mathbf { W } _ { i } ^ { K } , \mathbf { Z } ^ { l } \mathbf { W } _ { i } ^ { V } ) , } \end{array}
+$$
+
+where ${ \bf Z } ^ { 0 } = { \bf E }$ at the first layer; $\mathbf { W } ^ { O } \in \mathbb { R } ^ { d \times d }$ ; $\{ \mathbf { W } _ { i } ^ { Q } , \mathbf { W } _ { i } ^ { K } , \mathbf { W } _ { i } ^ { V } \}$ are weight matrices (in $\textstyle \mathbb { R } ^ { d \times { \frac { d } { h } } }$ ) of query, key, value of the $i$ -th head self-attention module.
+
+The multi-head attention output $\mathbf { Z } _ { \mathrm { a t t } } ^ { l }$ is further transformed by a token-wise gating layer as $\mathbf { g } ^ { l } =$ $\sigma ( \mathbf { Z } _ { \mathrm { a t t } } ^ { l } \mathbf { w } ^ { G } )$ , where $\sigma ( \cdot )$ is a sigmoid function; $\mathbf { g } ^ { l } \in [ 0 , 1 ] ^ { n }$ controls the magnitude of each token embedding before $\mathbf { Z } _ { \mathrm { a t t } }$ goes to the linear projection. This gates then filters the linear layer output
+
+$$
+\mathbf { Z } ^ { l + 1 } = \mathtt { L i n e a r } \left( ( \mathbf { g } ^ { l } \odot \mathbf { Z } _ { \mathrm { a t t } } ^ { l } ) \oplus \mathtt { L i n e a r } ( \mathbf { Z } _ { \mathrm { a t t } } ^ { l } ) \right)
+$$
+
+to obtain the transformer output $\mathbf { Z } ^ { l + 1 } \in \mathbb { R } ^ { n \times d }$ . This mechanism is learnt to focus on important features by redistributing the attention on tokens. The final [cls] embedding $\mathbf { z } ^ { [ c l s ] }$ at the $L$ -th layer is used by the classifier for prediction.
+
+# 2.4 Self-supervised and supervised pretraining of TransTab
+
+The input processor accepts variable-column tables, which opens the door for tabular pretraining on heterogeneous tables. In detail, TransTab is feasible for self-supervised and supervised pretraining.
+
+Self-supervised VPCL. Most SSL tabular methods work on the whole fixed set of columns [2, 24, 11], which take high computational costs and are prone to overfitting. Instead, we take tabular vertical partitions to build positive and negative samples for CL under the hypothesis that the powerful representation should model view-invariant factors. In detail, we subset columns as illustrated by Fig. 3 where Self-VPCL is on the top right. Suppose a sample $\mathbf { x } _ { i } = \{ \mathbf { v } _ { i } ^ { 1 } , \ldots , \mathbf { v } _ { i } ^ { K } \}$ with $K$ partitions $\mathbf { v } _ { i } ^ { k }$ . Neighbouring partitions can have overlapping regions which are justified by the percentage of columns of the partition. Self-VPCL takes partitions from the same sample as the positive and others as the negative:
+
+$$
+\ell ( \mathbf { X } ) = - \sum _ { i = 1 } ^ { B } \sum _ { k = 1 } ^ { K } \sum _ { k ^ { \prime } \neq k } ^ { K } \log \frac { \exp \psi ( \mathbf { v } _ { i } ^ { k } , \mathbf { v } _ { i } ^ { k ^ { \prime } } ) } { \sum _ { j = 1 } ^ { B } \sum _ { k ^ { \prime } = 1 } ^ { K } \exp \psi ( \mathbf { v } _ { i } ^ { k } , \mathbf { v } _ { j } ^ { k ^ { \dagger } } ) } ,
+$$
+
+where $B$ is the batch size; $\psi ( \cdot , \cdot )$ is the cosine similarity function. $\psi$ applies to $\hat { \mathbf { z } } ^ { [ c l s ] }$ which is the linear projection of partition $\mathbf { v }$ ’s embedding $\mathbf { z } ^ { [ c l s ] }$ . Compared with vanilla CL like SCARF [11], Self-VPCL significantly expand the positive and negative sampling for learning more robust and rich embeddings. What is more, this vertical partition sampling is extremely friendly to column-oriented databases [25] which support the fast querying a subset of columns from giant data warehouses. For the sake of computational efficiency, when $K > 2$ , we randomly sample two partitions.
+
+Supervised VPCL. When we own labeled tabular data for pretraining, one natural idea would be taking task-specific predicting heads for pretraining on vanilla supervised loss, e.g., crossentropy loss. In finetuning, these heads are dropped and a new head will be added on top of the pretrained encoder. However, we argue it is suboptimal and may undermine the model transferability. The reason behind is that tabular datasets vary dramatically in size, task definition, and class distributions. Pretraining TransTab using supervised loss inevitably causes the encoder biased to the major tasks and classes. Moreover, the suitable hyperparameter range is often distinct across tabular data when applying supervised loss. The same set of hyperparameters can cause overfitting on one dataset and underfitting on another. Therefore, it is tricky to pick appropriate hyperparameters for pretraining based on vanilla supervised loss.
+
+![](images/fb7e681a5cd0d8ec64c66eaae6c383b5034bccc8dc44cd56405bd3eaeb1d3a3b.jpg)  
+Figure 3: The demonstration of contrastive learning methods (different pieces can either be distinct or be overlapped partially). Self-VPCL: Positive pairs are partitions of the same sample; VPCL: Positive pairs are partitions of the sample belonging to the same class.
+
+In this paper, we propose VPCL for pretraining inspired by supervised CL [26] which was proved robust to noise and hyperparameters. As illustrated by Fig. 3, we build positive pairs considering views from the same class except for only from the same sample:
+
+$$
+\ell ( \mathbf { X } , \mathbf { y } ) = - \sum _ { i = 1 } ^ { B } \sum _ { j = 1 } ^ { B } \sum _ { k = 1 } ^ { K } \sum _ { k ^ { \prime } = 1 } ^ { K } \mathbf { 1 } \{ y _ { j } = y _ { i } \} \log { \frac { \exp \psi ( \mathbf { v } _ { i } ^ { k } , \mathbf { v } _ { j } ^ { k ^ { \prime } } ) } { \sum _ { j ^ { \prime } = 1 } ^ { B } \sum _ { k ^ { \prime } = 1 } ^ { K } \mathbf { 1 } \{ y _ { j ^ { \dagger } } \neq y _ { i } \} \exp \psi ( \mathbf { v } _ { i } ^ { k } , \mathbf { v } _ { j ^ { \dagger } } ^ { k ^ { \dagger } } ) } } .
+$$
+
+$\mathbf { y } = \{ y _ { i } \} _ { i } ^ { B }$ are labels; $\mathbf { 1 } \{ \cdot \}$ is indicator function. VPCL relieves multiple pretraining predictors required to adjust to different datasets. Moreover, VPCL exposes more feature embeddings to the supervision by partitioning hence providing more discriminative and generalizable representations.
+
+# 3 Experiments
+
+In this section, we aim at answering the following questions by extensive experiments:
+
+• Q1. How does TransTab perform compared with baselines under the vanilla supervised setting? • Q2. How well does TransTab address incremental columns from a stream of data (S(2) in Fig. 1)? • Q3. How is the impact of TransTab learned from multiple tables (with different columns) drawn from the same domain on its predictive ability (S(1) in Fig. 1)?
+
+Table 1: Statistics of the use clinical trial mortality prediction datasets. All are binary classification tasks. Positive ratio means the ratio of data points belong the positive class. NCTxxx are trial identifiers which can be linked to trials on ClinicalTrials.gov.   
+
+<table><tr><td>Name</td><td>Datapoints</td><td>Categorical</td><td>Binary</td><td>Numerical</td><td>Positive ratio</td></tr><tr><td>NCT00041119</td><td>3871</td><td>5</td><td>8</td><td>2</td><td>0.07</td></tr><tr><td>NCT00174655</td><td>994</td><td>3</td><td>31</td><td>15</td><td>0.02</td></tr><tr><td>NCT00312208</td><td>1651</td><td>5</td><td>12</td><td>6</td><td>0.19</td></tr><tr><td>NCT00079274</td><td>2968</td><td>5</td><td>8</td><td>3</td><td>0.12</td></tr><tr><td>NCT00694382</td><td>1604</td><td>1</td><td>29</td><td>11</td><td>0.45</td></tr></table>
+
+• Q4. Can TransTab be a zero-shot learner when pretrained on tables and infer on a new table (S(4) in Fig. 1)?
+
+• Q5. Is the proposed vertical partition CL better than vanilla supervised pretraining and selfsupervised CL (S(3) in Fig. 1)?
+
+Datasets. We introduce clinical trial mortality prediction datasets where each includes a distinct group of patients and columns 3. The data statistics are in Table 1. Accurately predicting the patient mortality in clinical trials is crucial because it helps identify catastrophic treatment then save patients from harm and improve the clinical trial design. Considering they are from a similar domain, we can utilize them to test if TransTab can achieve transfer learning. Besides, we also include a set of public tabular datasets, the statistics are in Table 7.
+
+Dataset pre-processing. For all baselines, we represent categorical features by ordinal encoding if they need to specify categorical features, otherwise one-hot encoding is used. Numerical features are scaled to $[ 0 , 1 ]$ by min-max normalization. Exceptionally for TransTab, we map the categorical feature index to its original description, e.g., mapping class "1" under "gender" to "female".
+
+Model and implementation protocols. Unless specified otherwise, we keep the settings fixed across all experiments. TransTab uses 2 layers of gated transformers where the embedding dimensions of numbers and tokens are 128, and the hidden dimension of intermediate dense layers is 256. The attention module has 8 heads. We choose ReLU activations and do not activate dropout. We train TransTab using Adam optimizer [27] with learning rate in $\{ 2 \mathrm { e } { - } 5 , 5 \mathrm { e } { - } 5 , 1 \mathrm { e } { - } 4 \}$ and no weight decay; batch size is in $\{ 1 6 , 6 4 , 1 2 8 \}$ . We set a maximum self-supervised pretraining epochs of 50 and supervised training epochs of 100. A patience of 10 is kept for supervised training for early stopping. Experiments were conducted with one RTX3070 GPU, i7-10700 CPU, and 16GB RAM.
+
+Baselines. We include the following baselines for comparison: Logistic regression $( L R )$ ; XGBoost [28]; Multilayer perceptron $( M L P )$ ; SeLU MLP (SNN) [29]; TabNet [30]; DCN [1]; AutoInt [31]; TabTransformer [5]; FT-Transformer [32]; VIME [2]; SCARF [11]. We provide the baseline architectures and implementations in Appendix B.
+
+# 3.1 Q1. Supervised learning
+
+Results of supervised learning on clinical trial mortality prediction datasets are summarized by Table 2. Note that all methods including ours do not perform pre-training. We see that our method outperforms baselines on all. From the view of method ranks, we surprisingly identify that LR wins over half of baseline methods. Except for TransTab, FT-Transformer is the only model that shows significant superiority over LR, which illustrates the potential of transformers for tabular modeling. Additional results on public datasets are available in Table 8 where we witness that our method is comparable to the state-of-the-art baseline tabular models. We also discover the baselines drawn from the CTR prediction literature (DCN and AutoInt) turn out the be competitive in tabular modeling.
+
+# 3.2 Q2. Feature incremental learning
+
+For previous tabular models, we should either drop new features or drop old data when confronting feature incremental learning. By contrast, TransTab is able to continually learn from new data with incremental features. We split the raw dataset into three subsets: set1, 2, and 3 which mimic the incremental feature scenario shown by (2) in Fig. 1. Baseline methods apply to two scenarios: (a) learning from all data that only have features of set1 and (b) learning from the data of set3 only. We report the best of the two. TransTab applies to learning from all three subsets. Table 3 shows the results where we find our method outperforms baselines by a great margin. It demonstrates that TransTab makes the best of incremental features to learn better. Similar observations appear in public datasets, shown by Table 9.
+
+Table 2: Test AUROC results on clinical trial mortality datasets the under supervised learning setting. All the remaining tables in this paper follow these setups to avoid clutter: the metric values are averaged over 10 random seeds; the Rank column reports the average rank across all datasets; Top results for each dataset are in bold.   
+
+<table><tr><td>Methods</td><td>N00041119</td><td>N00174655</td><td>N00312208</td><td>N00079274</td><td>N00694382</td><td>Rank(Std)</td></tr><tr><td>LR</td><td>0.6364</td><td>0.8543</td><td>0.7382</td><td>0.7067</td><td>0.7360</td><td>5.40(1.14)</td></tr><tr><td>XGBoost</td><td>0.5937</td><td>0.5000</td><td>0.6911</td><td>0.6784</td><td>0.7440</td><td>9.60(3.71)</td></tr><tr><td>MLP</td><td>0.6340</td><td>0.6189</td><td>0.7427</td><td>0.6967</td><td>0.7063</td><td>8.00(2.83)</td></tr><tr><td>SNN</td><td>0.6335</td><td>0.9130</td><td>0.7469</td><td>0.6948</td><td>0.7246</td><td>5.80(2.39)</td></tr><tr><td>TabNet</td><td>0.5856</td><td>0.5401</td><td>0.6910</td><td>0.6031</td><td>0.7113</td><td>11.40(0.89)</td></tr><tr><td>DCN</td><td>0.6349</td><td>0.7577</td><td>0.7431</td><td>0.6952</td><td>0.7458</td><td>5.60(2.51)</td></tr><tr><td>AutoInt</td><td>0.6327</td><td>0.7502</td><td>0.7479</td><td>0.6958</td><td>0.7411</td><td>6.20(2.59)</td></tr><tr><td>TabTrans</td><td>0.6187</td><td>0.9035</td><td>0.7069</td><td>0.7178</td><td>0.7229</td><td>7.20(3.56)</td></tr><tr><td>FT-Trans</td><td>0.6372</td><td>0.9073</td><td>0.7586</td><td>0.7090</td><td>0.7231</td><td>4.20(2.28)</td></tr><tr><td>VIME</td><td>0.6397</td><td>0.8533</td><td>0.7227</td><td>0.6790</td><td>0.7232</td><td>7.00(3.08)</td></tr><tr><td>SCARF</td><td>0.6248</td><td>0.9310</td><td>0.7267</td><td>0.7176</td><td>0.7103</td><td>6.60(3.91)</td></tr><tr><td>TransTab</td><td>0.6408</td><td>0.9428</td><td>0.7770</td><td>0.7281</td><td>0.7648</td><td>1.00(0.00)</td></tr></table>
+
+Table 3: Test AUROC results on clinical trial datasets under feature incremental learning.   
+
+<table><tr><td>Methods</td><td>N00041119</td><td>N00174655</td><td>N00312208</td><td>N00079274</td><td>N00694382</td><td>Rank(Std)</td></tr><tr><td>LR</td><td>0.6213</td><td>0.8485</td><td>0.6801</td><td>0.6258</td><td>0.7236</td><td>4.6(3.21)</td></tr><tr><td>XGBoost</td><td>0.5735</td><td>0.7890</td><td>0.6760</td><td>0.6038</td><td>0.6463</td><td>8.8(2.59)</td></tr><tr><td>MLP</td><td>0.6371</td><td>0.7754</td><td>0.6871</td><td>0.6220</td><td>0.6851</td><td>6.2(2.95)</td></tr><tr><td>SNN</td><td>0.5765</td><td>0.7440</td><td>0.6854</td><td>0.6336</td><td>0.7035</td><td>6.4(2.30)</td></tr><tr><td>TabNet</td><td>0.5548</td><td>0.8419</td><td>0.5849</td><td>0.6052</td><td>0.6668</td><td>9.0(3.39)</td></tr><tr><td>DCN</td><td>0.5172</td><td>0.5846</td><td>0.6640</td><td>0.6535</td><td>0.6957</td><td>8.2(4.16)</td></tr><tr><td>AutoInt</td><td>0.5232</td><td>0.6075</td><td>0.7031</td><td>0.6394</td><td>0.6974</td><td>7.2(3.56)</td></tr><tr><td>TabTrans</td><td>0.5599</td><td>0.7652</td><td>0.6433</td><td>0.6365</td><td>0.6841</td><td>8.2(1.10)</td></tr><tr><td>FT-Trans</td><td>0.5552</td><td>0.8045</td><td>0.7148</td><td>0.6471</td><td>0.6815</td><td>5.8(3.11)</td></tr><tr><td>VIME</td><td>0.6101</td><td>0.8114</td><td>0.3705</td><td>0.6444</td><td>0.6436</td><td>7.4(4.22)</td></tr><tr><td>SCARF</td><td>0.5996</td><td>0.6261</td><td>0.7072</td><td>0.6535</td><td>0.6957</td><td>5.2(2.97)</td></tr><tr><td>TransTab</td><td>0.6797</td><td>0.8545</td><td>0.7617</td><td>0.6857</td><td>0.7795</td><td>1.0(0.00)</td></tr></table>
+
+# 3.3 Q3. Transfer learning
+
+We further test if TransTab is able to transfer knowledge across tables. Results are in Table 4. We split each dataset into two subsets with $50 \%$ overlaps of their columns. Baselines are trained and tested on set1 (only label-supervision) or set2 separately. For our method we pretrain it on set1 then finetune it on set2 and report its performance on set2, and vice versa. We observe that TransTab can benefit from knowledge transfer across tables to reach superior performances. Similar observations are made on public datasets shown by Table 10.
+
+Table 4: Test AUROC results on clinical trial datasets under transfer learning across tables.   
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">N00041119</td><td colspan="2">NO0174655</td><td colspan="2">N00312208</td><td colspan="2">N00079274</td><td colspan="2">N00694382</td><td rowspan="2">Rank(Std)</td></tr><tr><td>set1</td><td>set2</td><td>set1</td><td>set2</td><td>set1</td><td>set2</td><td>set1</td><td>set2</td><td>set1</td><td>set2</td></tr><tr><td>LR</td><td>0.625</td><td>0.647</td><td>0.789</td><td>0.819</td><td>0.701</td><td>0.735</td><td>0.635</td><td>0.685</td><td>0.675</td><td>0.763</td><td>5.33(1.73)</td></tr><tr><td>XGBoost</td><td>0.638</td><td>0.575</td><td>0.574</td><td>0.886</td><td>0.690</td><td>0.700</td><td>0.596</td><td>0.647</td><td>0.592</td><td>0.677</td><td>7.56(3.75)</td></tr><tr><td>MLP</td><td>0.639</td><td>0.621</td><td>0.314</td><td>0.857</td><td>0.683</td><td>0.744</td><td>0.620</td><td>0.675</td><td>0.648</td><td>0.765</td><td>6.56(3.32)</td></tr><tr><td>SNN</td><td>0.627</td><td>0.634</td><td>0.215</td><td>0.754</td><td>0.687</td><td>0.732</td><td>0.631</td><td>0.683</td><td>0.651</td><td>0.759</td><td>7.44(2.07)</td></tr><tr><td>TabNet</td><td>0.564</td><td>0.558</td><td>0.856</td><td>0.592</td><td>0.671</td><td>0.657</td><td>0.443</td><td>0.605</td><td>0.581</td><td>0.677</td><td>10.67(2.96)</td></tr><tr><td>DCN</td><td>0.636</td><td>0.625</td><td>0.767</td><td>0.790</td><td>0.711</td><td>0.698</td><td>0.682</td><td>0.664</td><td>0.658</td><td>0.737</td><td>6.33(2.45)</td></tr><tr><td>AutoInt</td><td>0.629</td><td>0.630</td><td>0.843</td><td>0.730</td><td>0.725</td><td>0.698</td><td>0.679</td><td>0.665</td><td>0.686</td><td>0.661</td><td>5.89(2.89)</td></tr><tr><td>TabTrans</td><td>0.616</td><td>0.647</td><td>0.866</td><td>0.822</td><td>0.675</td><td>0.677</td><td>0.618</td><td>0.702</td><td>0.652</td><td>0.718</td><td>6.22(3.38)</td></tr><tr><td>FT-Trans</td><td>0.627</td><td>0.641</td><td>0.836</td><td>0.858</td><td>0.720</td><td>0.741</td><td>0.692</td><td>0.692</td><td>0.652</td><td>0.740</td><td>4.22(2.28)</td></tr><tr><td>VIME</td><td>0.603</td><td>0.625</td><td>0.312</td><td>0.726</td><td>0.601</td><td>0.642</td><td>0.477</td><td>0.668</td><td>0.614</td><td>0.715</td><td>10.44(1.51)</td></tr><tr><td>SCARF</td><td>0.635</td><td>0.657</td><td>0.651</td><td>0.814</td><td>0.653</td><td>0.686</td><td>0.682</td><td>0.701</td><td>0.671</td><td>0.776</td><td>5.56(3.40)</td></tr><tr><td>TransTab</td><td>0.653</td><td>0.653</td><td>0.904</td><td>0.846</td><td>0.730</td><td>0.756</td><td>0.680</td><td>0.711</td><td>0.747</td><td>0.774</td><td>1.78(1.30)</td></tr></table>
+
+Table 5: Test AUROC results on clinical trial datasets under zero-shot learning setting.   
+
+<table><tr><td>TransTab</td><td>N00041119</td><td>N00174655</td><td>N00312208</td><td>N00079274</td><td>N00694382</td></tr><tr><td>Supervised</td><td>0.5854</td><td>0.6484</td><td>0.7536</td><td>0.7087</td><td>0.6479</td></tr><tr><td>Transfer</td><td>0.6130</td><td>0.6909</td><td>0.7658</td><td>0.7163</td><td>0.6752</td></tr><tr><td>Zero-shot</td><td>0.5990</td><td>0.6752</td><td>0.7576</td><td>0.7036</td><td>0.6740</td></tr></table>
+
+# 3.4 Q4. Zero-shot learning
+
+Although there are numerous papers on zero-shot learning (ZSL) in CV and NLP [33, 34, 35], we notice that ZSL was hardly mentioned in tabular domain. In this experiment, we refer to the ZSL scenario mentioned by S(4) of Fig. 1 where we split the raw table into three equal-size subsets. Three subsets have distinct columns. For the zero-shot setting, the model learns from set1+set2 and is tested on set3 without further training. In this scenario, the model needs to leverage the learned knowledge from set1 and set2 to support the inference on a new table set3. Besides, we design two baselines for comparison: supervised where the model learns from set3 and predicts on set3 and transfer where the model learns from set1 $^ +$ set2 and continues to be finetuned on set3. Results are in Table 5. We surprisingly find the ZSL model gets better performance than the supervised one on average. It boils down to that (1) ZSL TransTab succeeds to retain the learned knowledge from set1+set2 for predicting on a new table (set3) and (2) ZSL can benefit from more data (set1 $^ +$ set2) than the supervised (set3 only). Meanwhile, the transfer model takes the advantage of set1 $^ +$ set2 and is adapted for set3 by finetuning, hence reaches the best performance. Similarly, we witness that TransTab is able to make zero-shot predictions on public datasets as in Table 11.
+
+Additional sensitivity check is provided by Fig. 6 where we vary the overlap ratio of two subsets from the same dataset. We witness that our model makes reasonable predictions even if the training set has no column overlap with the test set.
+
+# 3.5 Q5. Supervised and self-supervised pretraining
+
+We take experiments to compare the proposed VPCL with the vanilla transfer learning strategy, as in Table 6. We observe that the vanilla strategy harms the performance on two datasets while VPCL always brings positive effect for finetuning. Besides, we conduct experiments on varying the number of partitions and show the average AUROC on all five datasets, shown by Fig. 4. We specify that VPCL demonstrates an advantage over self-VPCL when we increase the partition numbers.
+
+We also explore if pretraining works on public datasets. Results in Table 12 somewhat match our expectations that pretraining on unrelated tabular data usually yields few benefits for finetuning because these tables define totally different columns and targeted tasks. We also show the ablation on the number of partitions by Fig. 5 where VPCL consistently outperforms the Supervised baseline.
+
+Table 6: Test AUROC on clinical trial datasets under the across-table pretraining plus finetuning setting. Supervised: baseline supervised model; Transfer: vanilla supervised transfer learning. Red shows the one worse than the Supervised baseline.   
+
+<table><tr><td>TransTab</td><td>N00041119</td><td>N00174655</td><td>NO0312208</td><td>NO0079274</td><td>N00694382</td></tr><tr><td>Supervised</td><td>0.6313</td><td>0.8348</td><td>0.7444</td><td>0.6885</td><td>0.7293</td></tr><tr><td>Transfer</td><td>0.6424</td><td>0.8183</td><td>0.7458</td><td>0.6928</td><td>0.7239</td></tr><tr><td>Self-VPCL</td><td>0.6412</td><td>0.8577</td><td>0.7486</td><td>0.7069</td><td>0.7348</td></tr><tr><td>VPCL</td><td>0.6405</td><td>0.8583</td><td>0.7517</td><td>0.7063</td><td>0.7392</td></tr></table>
+
+Nevertheless, it is still worth investigating the table phenotypes to aggregate tables which are more likely to benefit from each other by transfer learning.
+
+# 4 Related Works
+
+Tabular Prediction. To enhance tabular predictions, numerous recent works try to design new algorithms [28, 36, 37, 30, 38, 32, 5, 10, 7, 39, 40, 41, 42, 43, 44, 45]. However, it was argued that boosting algorithms and MLPs are still the competitive choices for tabular data modeling, especially when the sample size is small [32, 46, 39, 47]. To alleviate label scarcity issue, SSL pretraining on unlabeled tabular data was introduced [2, 24, 10, 9, 11]. Nonetheless, none of them is transferable across tables then is able to extend the success of pretraining to the tabular domain. For practical tabular predictions, the common case is that we own a lot of labeled samples collected with diverse protocols hence heavy preprocessing is needed to align them by either dropping many samples or many features. By contrast, TransTab accepts variable-column tables and therefore can learn from different tables at scale and transfer to the target task. Also, it can support diverse tabular prediction tasks as depicted in Fig. 1, which cannot be done by off-the-shelf tabular methods.
+
+Transfer learning. Transfer learning (TL) has long been a popular research field since the proposal of ImageNet [48], which gives rise to splendid works on utilizing supervised pretraining on a large general database and finetune on a small downstream task [49, 50, 51, 52, 53]. TL is also fast-growing in NLP beginning at BERT [20], which often leverages web-scale unlabeled texts for self-supervised pretraining and then applies to specific tasks [34, 54, 55, 56, 57]. However, few work was on TL in tabular predictions. As mentioned in $\ S$ , TransTab paves the way for effective tabular TL by establishing a feature processing protocol that applies for most table inputs, such that it shares knowledge across tables.
+
+Self-supervised learning & contrastive learning. SSL uses unlabeled data with pretext tasks to learn useful representations and most of them are in CV and NLP [20, 17, 15, 16, 58, 23, 59, 60, 61, 62, 63]. Recent SSL tabular models can be classified into reconstruction and contrastive based methods: TabNet [30] and VIME [2] try to recover the corrupted inputs with auto-encoding loss; SCARF [11] takes a SimCLR-like [64] contrastive loss between the sample and its corrupted version; SubTab [9] takes a combination of both. Nevertheless, all fail to learn transferable models across tables such that cannot benefit from pretraining with scale. Contrastive learning can also be applied to supervised learning by leveraging class labels to build positive samples [26]. Our work extends it to to the tabular domain, which we prove works better than vanilla supervised pretraining. The vertical partition sampling also enjoys high query speed from large databases which are often column-oriented [25]. Another line of research takes table pretraining table semantic parsing [65, 66, 67, 68, 69] or table-to-text generation [70, 71]. But these methods either encode the whole table instead of each row or do not demonstrate to benefit tabular prediction yet.
+
+# 5 Conclusion
+
+This paper proposes TransTab that accepts variable-column inputs. By the proposed vertical partition contrastive learning, it can benefit from supervised pretraining from multiple tabular datasets with low memory cost. We envision it to be the basis of tabular foundation models and widely used to tabular-related applications in the future.
+
+# Acknowledgement
+
+This work was supported by NSF award SCH-2205289, SCH-2014438, IIS-1838042, NIH award R01 1R01NS107291-01.
+
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+
+# Checklist
+
+1. For all authors...
+
+(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]   
+(b) Did you describe the limitations of your work? [Yes] See $\ S \ 3 . 5$ and Appendix $\ S \mathrm { A }$ .   
+(c) Did you discuss any potential negative societal impacts of your work? [Yes] See Appendix $\ S \mathrm { A }$ .   
+(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
+
+2. If you are including theoretical results...
+
+(a) Did you state the full set of assumptions of all theoretical results? [N/A] This paper does not include theoretical results.   
+(b) Did you include complete proofs of all theoretical results? [N/A] This paper does not include theoretical results.
+
+3. If you ran experiments...
+
+(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] See supplementary materials.   
+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] For our methods please see Model and Implementation Protocols of $\ S$ ; for the compared baselines please see Appendix $\ S _ { \mathrm { B } }$ ;   
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes]   
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] Please see Model and Implementation Protocols of $\ S 3$ .
+
+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+
+(a) If your work uses existing assets, did you cite the creators? [Yes] See Table 13.
+
+(b) Did you mention the license of the assets? [Yes] Licenses are available referring to the provided links.   
+(c) Did you include any new assets either in the supplemental material or as a URL? [Yes] See Appendix $\ S C$ .   
+(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [Yes] See Appendix $\ S$ .   
+(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [Yes] See Appendix $\ S C$ .
+
+5. If you used crowdsourcing or conducted research with human subjects...
+
+(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A] This paper does not use crowdsourcing.   
+(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A] This paper does not use crowdsourcing.   
+(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A] This paper does not use crowdsourcing.

parse/dev/A1yGs_SWiIi/A1yGs_SWiIi_content_list.json

@@ -0,0 +1,1204 @@
+[
+    {
+        "type": "text",
+        "text": "TransTab: Learning Transferable Tabular Transformers Across Tables ",
+        "text_level": 1,
+        "bbox": [
+            245,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Zifeng Wang1 and Jimeng $\\mathbf { S u n ^ { 1 , 2 } }$   \n1 Department of Computer Science, University of Illinois Urbana-Champaign   \n2 Carle Illinois College of Medicine, University of Illinois Urbana-Champaign {zifengw2,jimeng}@illinois.edu ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            314,
+            535,
+            330
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Tabular data (or tables) are the most widely used data format in machine learning (ML). However, ML models often assume the table structure keeps fixed in training and testing. Before ML modeling, heavy data cleaning is required to merge disparate tables with different columns. This preprocessing often incurs significant data waste (e.g., removing unmatched columns and samples). How to learn ML models from multiple tables with partially overlapping columns? How to incrementally update ML models as more columns become available over time? Can we leverage model pretraining on multiple distinct tables? How to train an ML model which can predict on an unseen table? ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "To answer all those questions, we propose to relax fixed table structures by introducing a Transferable Tabular Transformer (TransTab) for tables. The goal of TransTab is to convert each sample (a row in the table) to a generalizable embedding vector, and then apply stacked transformers for feature encoding. One methodology insight is combining column description and table cells as the raw input to a gated transformer model. The other insight is to introduce supervised and self-supervised pretraining to improve model performance. We compare TransTab with multiple baseline methods on diverse benchmark datasets and five oncology clinical trial datasets. Overall, TransTab ranks 1.00, 1.00, 1.78 out of 12 methods in supervised learning, feature incremental learning, and transfer learning scenarios, respectively; and the proposed pretraining leads to $2 . 3 \\%$ AUC lift on average over the supervised learning. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Tabular data are ubiquitous in healthcare, engineering, advertising, and finance [1, 2, 3, 4]. They are often stored in a relational database as tables or spreadsheets. Table rows represent the data samples, and columns represent the feature variables of diverse data types (e.g., categorical, numerical, binary, and textual). Recent works enhance tabular ML modeling using deep networks [5, 6, 7, 8] or designing self-supervision [2, 9, 10, 11]. Those existing works require the same table structure in training and testing data. However, there can be multiple tables sharing partially overlapped columns in the real world. Hence, learning across tables is inapplicable. The traditional remedy is to perform data cleaning by removing non-overlapping columns and mismatched samples before training any ML models, which waste data resources [12, 13, 14]. Therefore, learning across tables with disparate columns and transferring knowledge across tables are crucial to extending the success of deep learning/pretraining to the tabular domain. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Tables are highly structured yet flexible. The first step to achieve learning across tables is to rethink the basic elements in tabular data modeling. In computer vision, the basic elements are pixels [15] or patches, [16, 17]; in natural language processing (NLP), the basic elements are words [18] or tokens [19, 20]. In the tabular domain, it is natural to treat cells in each column as independent elements. Columns are mapped to unique indexes then models take the cell values for training and inference. The premise of this modeling formulation is to keep the same column structure in all the tables. But tables often have divergent protocols where the nomenclatures of columns and cells differ. By contrast, our proposed work contextualizes the columns and cells. For example, previous methods represent a cell valued man under the column gender by 0 referring to the codebook $\\mathbf { \\bar { \\{ m a n : 0 , w o m a n : 1 \\} } }$ . Our model converts the tabular input into a sequence input (e.g., gender is man), which can be modeled with downstream sequence models. We argue such featurizing protocol is generalizable across tables, thus enabling models to apply to different tables. ",
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/94370f31a56015ca1ba3db4876b8cebf454e8075065c1dee5e6f0926c6c4024f.jpg",
+        "image_caption": [
+            "Figure 1: The demonstration of ML modeling on different tabular data settings. Previous tabular methods only do vanilla supervised training or pretraining on the same table due to they only accept fixed-column tables. By contrast, TransTab covers more new tasks (1) to (4) as it accepts variablecolumn tables. Details are presented in $\\ S$ . "
+        ],
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+        "text": "",
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "In a nutshell, we propose Transferable Transformers for Tabular analysis (TransTab), a versatile tabular learning framework 1. TransTab applies to multiple use cases as shown in Fig. 1. The key contributions behind TransTab are ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "• A systematic featurizing pipeline considering both column and cell semantics which is shared as the fundamental protocol across tables.   \n• Vertical-Partition Contrastive Learning (VPCL) that enables pretraining on multiple tables and also allows finetuning on target datasets. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "As shown by Fig. 1, due to the fixed-column assumption, all existing works only handle supervised learning or pretraining on the same-structure tables. On the contrary, TransTab relaxes this assumption and applies to four additional scenarios, which we will elaborate on in $\\ S 2 . 1$ . ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 Method ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this section, we present the details of TransTab. Fig. 2 illustrates its workflow including the following key components: 1) The input processor featurizes and embeds arbitrary tabular inputs to token-level embeddings; 2) The stacked gated transformer layers further encode the token-level embeddings; 3) Finally, the learning module includes a classifier trained on labeled data and a projector for contrastive learning. Next we will present the details of each component. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/2360345762e6c294b96a93e4f1190d24972776eeff0bcde0aff58b8ece6f1627.jpg",
+        "image_caption": [
+            "Figure 2: The demonstration of TransTab framework. the input processor encodes the sample into the token-level embedding $\\mathbf { E }$ ; the [cls] embedding $\\mathbf { z } ^ { [ c l s ] }$ in the representation $\\mathbf { Z } ^ { L }$ after $L$ gated transformer layers is used for prediction and learning. In supervised learning, $\\mathbf { z } ^ { [ c l s ] }$ is leveraged by a classifier to make predictions of target $y$ ; in contrastive learning, the projected $\\hat { \\mathbf { z } } ^ { [ c l s ] }$ is is used for self or supervised contrastive loss. "
+        ],
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.1 Application scenarios of TransTab ",
+        "text_level": 1,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Before presenting our method in details, we first introduce four novel applications scenarios which are tractable by TransTab, as shown in Fig. 1. Suppose we aim to predict the treatment efficacy for breast cancer trials using multiple clinical trial tables, here are several scenarios we often encounter. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "S(1) Transfer learning. We collect data tables from multiple cancer trials for testing the efficacy of the same drug on different patients. These tables were designed independently with overlapping columns. How do we learn ML models for one trial by leveraging tables from all trials? ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "S(2) Incremental learning. Additional columns might be added over time. For example, additional features are collected across different trial phases. How do we update the ML models using tables from all trial phases? ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "S(3) Pretraining+Finetuning. The trial outcome label (e.g., mortality) might not be always available from all table sources. Can we benefit pretraining on those tables without labels? How do we finetune the model on the target table with labels? ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "S(4) Zero-shot inference. We model the drug efficacy based on our trial records. The next step is to conduct inference with the model to find patients that can benefit from the drug. However, patient tables do not share the same columns as trial tables so direct inference is not possible. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Overall, we witness that the assumption of fixed table structure is the obstacle to use ML for various applications. Next we will present TransTab and demonstrate how it addresses these scenarios. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2.2 Input processor for columns and cells ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We build the input processor (1) to accept variable-column tables (2) to retain knowledge across tabular datasets. The idea is to convert tabular data (cells in columns) into a sequence of semantically encoded tokens. We utilize the following observation to create the sequence: the column description (e.g., column name) decides the meaning of cells in that column. For example, if a cell in column smoking history has value 1, it indicates the individual has a smoking history. Similarly, cell value 60 in column weight indicates $6 0 \\mathrm { k g }$ in weight instead of 60 years old. Motivated by the discussion, we propose to include column names into the tabular modeling. As a result, TransTab treats any tabular data as the composition of three elements: text (for categorical & textual cells and column names), continuous values (for numerical cells), and boolean values (for binary cells) . Fig. 2 illustrates a visual example of how these elements are leveraged to process the four basic types of features: categorical/textual cat, binary bin, and numerical num. ",
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+    {
+        "type": "text",
+        "text": "Categorical/Textual feature. A category or textual feature contains a sequence of text tokens. For the categorical feature cat, we concatenate the column name with the feature value $x _ { c }$ , which forms as a sequence of tokens. This sentence is then tokenized and matched to the token embedding matrix to generate the feature embedding $\\mathbf { E } _ { c } \\in \\mathbb { R } ^ { n _ { c } \\times d }$ where $d$ is the embedding dimension and $n _ { c }$ is the number of tokens. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Binary feature. The binary feature bin is usually an assertive description and its value $x _ { b } \\in \\{ 0 , 1 \\}$ . If $x _ { b } = 1$ , then bin is tokenized and encoded to the embeddings $\\mathbf { E } _ { b } \\in \\mathbb { R } ^ { n _ { b } \\times d }$ ; if not, it will not be processed to the subsequent steps. This design significantly reduces the computational and memory cost when the inputs have high-dimensional and sparse one-hot features. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Numerical feature. We do not concatenate column names and values for numerical feature because the tokenization-embedding paradigm was notoriously known to be bad at discriminating numbers [21]. Instead, we process them separately. num is encoded as same as cat and bin to get $\\mathbf { E } _ { u , c o l } \\in$ $\\mathbb { R } ^ { n _ { u } \\times d }$ . We then multiply the numerical features with the column embedding to yield the numerical embedding as $\\mathbf { E } _ { u } = x _ { u } ^ { \\top } \\times \\mathbf { E } _ { u , c o l } { } ^ { 2 }$ , which we identify gets an edge on more complicated numerical embedding techniques empirically. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "At last, $\\mathbf { E } _ { c }$ , $\\mathbf { E } _ { u }$ , $\\mathbf { E } _ { b }$ all pass the layer normalization [22] and the same linear layer to be aligned to the same space, then are concatenated with [cls] embedding to yield $\\mathbf { E } = \\tilde { \\mathbf { E } } _ { c } \\otimes \\tilde { \\mathbf { E } } _ { u } \\otimes \\tilde { \\mathbf { E } } _ { b } \\otimes \\mathbf { e } ^ { [ c l s ] }$ . ",
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+    },
+    {
+        "type": "text",
+        "text": "As a result, all cell values are contextualized regarding the corresponding column properties thus the semantic meaning of one element can vary depending on the context composition. This formulation benefits the knowledge transfer across tables a lot. For example, previously smoked depicts the same thing as smoking history. Previous methods never capture this connection while it is possible for TransTab to learn to recognize that 1 under both columns are equivalent. ",
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+    {
+        "type": "text",
+        "text": "2.3 Gated transformers ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The gated tabular transformer is an adaption of the classical transformer in NLP [23]. It consists of two main components: multi-head self-attention layer and gated feedforward layers. The input representation $\\mathbf { Z } ^ { l }$ at the $l$ -th layer is first adopted for exploring interactions between features: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c06601b70c52467041eb2c8e603967ddfa666e953351097aee9885c08466ae08.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathbf { Z } _ { \\mathrm { a t t } } ^ { l } = \\mathbb { M } \\mathrm { u } \\mathrm { 1 t i } \\mathrm { H e a d } \\mathrm { A t t n } ( \\mathbf { Z } ^ { l } ) = [ \\mathrm { h e a d } _ { 1 } , \\mathrm { h e a d } _ { 2 } , \\dots , \\mathrm { h e a d } _ { h } ] \\mathbf { W } ^ { O } , } \\\\ { \\mathrm { h e a d } _ { i } = \\mathrm { A t t e n t i o n } ( \\mathbf { Z } ^ { l } \\mathbf { W } _ { i } ^ { Q } , \\mathbf { Z } ^ { l } \\mathbf { W } _ { i } ^ { K } , \\mathbf { Z } ^ { l } \\mathbf { W } _ { i } ^ { V } ) , } \\end{array}\n$$",
+        "text_format": "latex",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where ${ \\bf Z } ^ { 0 } = { \\bf E }$ at the first layer; $\\mathbf { W } ^ { O } \\in \\mathbb { R } ^ { d \\times d }$ ; $\\{ \\mathbf { W } _ { i } ^ { Q } , \\mathbf { W } _ { i } ^ { K } , \\mathbf { W } _ { i } ^ { V } \\}$ are weight matrices (in $\\textstyle \\mathbb { R } ^ { d \\times { \\frac { d } { h } } }$ ) of query, key, value of the $i$ -th head self-attention module. ",
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+        "type": "text",
+        "text": "The multi-head attention output $\\mathbf { Z } _ { \\mathrm { a t t } } ^ { l }$ is further transformed by a token-wise gating layer as $\\mathbf { g } ^ { l } =$ $\\sigma ( \\mathbf { Z } _ { \\mathrm { a t t } } ^ { l } \\mathbf { w } ^ { G } )$ , where $\\sigma ( \\cdot )$ is a sigmoid function; $\\mathbf { g } ^ { l } \\in [ 0 , 1 ] ^ { n }$ controls the magnitude of each token embedding before $\\mathbf { Z } _ { \\mathrm { a t t } }$ goes to the linear projection. This gates then filters the linear layer output ",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/484a8cc744a8d2186562500b09b5cbb68d210c6998b30bf2f081c3308de90b37.jpg",
+        "text": "$$\n\\mathbf { Z } ^ { l + 1 } = \\mathtt { L i n e a r } \\left( ( \\mathbf { g } ^ { l } \\odot \\mathbf { Z } _ { \\mathrm { a t t } } ^ { l } ) \\oplus \\mathtt { L i n e a r } ( \\mathbf { Z } _ { \\mathrm { a t t } } ^ { l } ) \\right)\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "to obtain the transformer output $\\mathbf { Z } ^ { l + 1 } \\in \\mathbb { R } ^ { n \\times d }$ . This mechanism is learnt to focus on important features by redistributing the attention on tokens. The final [cls] embedding $\\mathbf { z } ^ { [ c l s ] }$ at the $L$ -th layer is used by the classifier for prediction. ",
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+    {
+        "type": "text",
+        "text": "2.4 Self-supervised and supervised pretraining of TransTab ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The input processor accepts variable-column tables, which opens the door for tabular pretraining on heterogeneous tables. In detail, TransTab is feasible for self-supervised and supervised pretraining. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Self-supervised VPCL. Most SSL tabular methods work on the whole fixed set of columns [2, 24, 11], which take high computational costs and are prone to overfitting. Instead, we take tabular vertical partitions to build positive and negative samples for CL under the hypothesis that the powerful representation should model view-invariant factors. In detail, we subset columns as illustrated by Fig. 3 where Self-VPCL is on the top right. Suppose a sample $\\mathbf { x } _ { i } = \\{ \\mathbf { v } _ { i } ^ { 1 } , \\ldots , \\mathbf { v } _ { i } ^ { K } \\}$ with $K$ partitions $\\mathbf { v } _ { i } ^ { k }$ . Neighbouring partitions can have overlapping regions which are justified by the percentage of columns of the partition. Self-VPCL takes partitions from the same sample as the positive and others as the negative: ",
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+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/b1565a55da01b92305142a53f706a6855116a77c0372e422383f026f3c5eb253.jpg",
+        "text": "$$\n\\ell ( \\mathbf { X } ) = - \\sum _ { i = 1 } ^ { B } \\sum _ { k = 1 } ^ { K } \\sum _ { k ^ { \\prime } \\neq k } ^ { K } \\log \\frac { \\exp \\psi ( \\mathbf { v } _ { i } ^ { k } , \\mathbf { v } _ { i } ^ { k ^ { \\prime } } ) } { \\sum _ { j = 1 } ^ { B } \\sum _ { k ^ { \\prime } = 1 } ^ { K } \\exp \\psi ( \\mathbf { v } _ { i } ^ { k } , \\mathbf { v } _ { j } ^ { k ^ { \\dagger } } ) } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            303,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $B$ is the batch size; $\\psi ( \\cdot , \\cdot )$ is the cosine similarity function. $\\psi$ applies to $\\hat { \\mathbf { z } } ^ { [ c l s ] }$ which is the linear projection of partition $\\mathbf { v }$ ’s embedding $\\mathbf { z } ^ { [ c l s ] }$ . Compared with vanilla CL like SCARF [11], Self-VPCL significantly expand the positive and negative sampling for learning more robust and rich embeddings. What is more, this vertical partition sampling is extremely friendly to column-oriented databases [25] which support the fast querying a subset of columns from giant data warehouses. For the sake of computational efficiency, when $K > 2$ , we randomly sample two partitions. ",
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+        "type": "text",
+        "text": "Supervised VPCL. When we own labeled tabular data for pretraining, one natural idea would be taking task-specific predicting heads for pretraining on vanilla supervised loss, e.g., crossentropy loss. In finetuning, these heads are dropped and a new head will be added on top of the pretrained encoder. However, we argue it is suboptimal and may undermine the model transferability. The reason behind is that tabular datasets vary dramatically in size, task definition, and class distributions. Pretraining TransTab using supervised loss inevitably causes the encoder biased to the major tasks and classes. Moreover, the suitable hyperparameter range is often distinct across tabular data when applying supervised loss. The same set of hyperparameters can cause overfitting on one dataset and underfitting on another. Therefore, it is tricky to pick appropriate hyperparameters for pretraining based on vanilla supervised loss. ",
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+        "type": "image",
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+        "image_caption": [
+            "Figure 3: The demonstration of contrastive learning methods (different pieces can either be distinct or be overlapped partially). Self-VPCL: Positive pairs are partitions of the same sample; VPCL: Positive pairs are partitions of the sample belonging to the same class. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "type": "text",
+        "text": "In this paper, we propose VPCL for pretraining inspired by supervised CL [26] which was proved robust to noise and hyperparameters. As illustrated by Fig. 3, we build positive pairs considering views from the same class except for only from the same sample: ",
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+        "type": "equation",
+        "img_path": "images/04916ae29e715e5f92631242502d00c607ef54907150dd0fcb3de898b409a3cf.jpg",
+        "text": "$$\n\\ell ( \\mathbf { X } , \\mathbf { y } ) = - \\sum _ { i = 1 } ^ { B } \\sum _ { j = 1 } ^ { B } \\sum _ { k = 1 } ^ { K } \\sum _ { k ^ { \\prime } = 1 } ^ { K } \\mathbf { 1 } \\{ y _ { j } = y _ { i } \\} \\log { \\frac { \\exp \\psi ( \\mathbf { v } _ { i } ^ { k } , \\mathbf { v } _ { j } ^ { k ^ { \\prime } } ) } { \\sum _ { j ^ { \\prime } = 1 } ^ { B } \\sum _ { k ^ { \\prime } = 1 } ^ { K } \\mathbf { 1 } \\{ y _ { j ^ { \\dagger } } \\neq y _ { i } \\} \\exp \\psi ( \\mathbf { v } _ { i } ^ { k } , \\mathbf { v } _ { j ^ { \\dagger } } ^ { k ^ { \\dagger } } ) } } .\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "$\\mathbf { y } = \\{ y _ { i } \\} _ { i } ^ { B }$ are labels; $\\mathbf { 1 } \\{ \\cdot \\}$ is indicator function. VPCL relieves multiple pretraining predictors required to adjust to different datasets. Moreover, VPCL exposes more feature embeddings to the supervision by partitioning hence providing more discriminative and generalizable representations. ",
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+    {
+        "type": "text",
+        "text": "3 Experiments ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "In this section, we aim at answering the following questions by extensive experiments: ",
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+    {
+        "type": "text",
+        "text": "• Q1. How does TransTab perform compared with baselines under the vanilla supervised setting? • Q2. How well does TransTab address incremental columns from a stream of data (S(2) in Fig. 1)? • Q3. How is the impact of TransTab learned from multiple tables (with different columns) drawn from the same domain on its predictive ability (S(1) in Fig. 1)? ",
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+        "type": "table",
+        "img_path": "images/91743883bd7e9c4f4f076a87b72e94af9b13dbe96acfacce2a88b91fd26fe7a6.jpg",
+        "table_caption": [
+            "Table 1: Statistics of the use clinical trial mortality prediction datasets. All are binary classification tasks. Positive ratio means the ratio of data points belong the positive class. NCTxxx are trial identifiers which can be linked to trials on ClinicalTrials.gov. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Name</td><td>Datapoints</td><td>Categorical</td><td>Binary</td><td>Numerical</td><td>Positive ratio</td></tr><tr><td>NCT00041119</td><td>3871</td><td>5</td><td>8</td><td>2</td><td>0.07</td></tr><tr><td>NCT00174655</td><td>994</td><td>3</td><td>31</td><td>15</td><td>0.02</td></tr><tr><td>NCT00312208</td><td>1651</td><td>5</td><td>12</td><td>6</td><td>0.19</td></tr><tr><td>NCT00079274</td><td>2968</td><td>5</td><td>8</td><td>3</td><td>0.12</td></tr><tr><td>NCT00694382</td><td>1604</td><td>1</td><td>29</td><td>11</td><td>0.45</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "• Q4. Can TransTab be a zero-shot learner when pretrained on tables and infer on a new table (S(4) in Fig. 1)? ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "• Q5. Is the proposed vertical partition CL better than vanilla supervised pretraining and selfsupervised CL (S(3) in Fig. 1)? ",
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+    {
+        "type": "text",
+        "text": "Datasets. We introduce clinical trial mortality prediction datasets where each includes a distinct group of patients and columns 3. The data statistics are in Table 1. Accurately predicting the patient mortality in clinical trials is crucial because it helps identify catastrophic treatment then save patients from harm and improve the clinical trial design. Considering they are from a similar domain, we can utilize them to test if TransTab can achieve transfer learning. Besides, we also include a set of public tabular datasets, the statistics are in Table 7. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Dataset pre-processing. For all baselines, we represent categorical features by ordinal encoding if they need to specify categorical features, otherwise one-hot encoding is used. Numerical features are scaled to $[ 0 , 1 ]$ by min-max normalization. Exceptionally for TransTab, we map the categorical feature index to its original description, e.g., mapping class \"1\" under \"gender\" to \"female\". ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Model and implementation protocols. Unless specified otherwise, we keep the settings fixed across all experiments. TransTab uses 2 layers of gated transformers where the embedding dimensions of numbers and tokens are 128, and the hidden dimension of intermediate dense layers is 256. The attention module has 8 heads. We choose ReLU activations and do not activate dropout. We train TransTab using Adam optimizer [27] with learning rate in $\\{ 2 \\mathrm { e } { - } 5 , 5 \\mathrm { e } { - } 5 , 1 \\mathrm { e } { - } 4 \\}$ and no weight decay; batch size is in $\\{ 1 6 , 6 4 , 1 2 8 \\}$ . We set a maximum self-supervised pretraining epochs of 50 and supervised training epochs of 100. A patience of 10 is kept for supervised training for early stopping. Experiments were conducted with one RTX3070 GPU, i7-10700 CPU, and 16GB RAM. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Baselines. We include the following baselines for comparison: Logistic regression $( L R )$ ; XGBoost [28]; Multilayer perceptron $( M L P )$ ; SeLU MLP (SNN) [29]; TabNet [30]; DCN [1]; AutoInt [31]; TabTransformer [5]; FT-Transformer [32]; VIME [2]; SCARF [11]. We provide the baseline architectures and implementations in Appendix B. ",
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+    {
+        "type": "text",
+        "text": "3.1 Q1. Supervised learning ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Results of supervised learning on clinical trial mortality prediction datasets are summarized by Table 2. Note that all methods including ours do not perform pre-training. We see that our method outperforms baselines on all. From the view of method ranks, we surprisingly identify that LR wins over half of baseline methods. Except for TransTab, FT-Transformer is the only model that shows significant superiority over LR, which illustrates the potential of transformers for tabular modeling. Additional results on public datasets are available in Table 8 where we witness that our method is comparable to the state-of-the-art baseline tabular models. We also discover the baselines drawn from the CTR prediction literature (DCN and AutoInt) turn out the be competitive in tabular modeling. ",
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+    {
+        "type": "text",
+        "text": "3.2 Q2. Feature incremental learning ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "For previous tabular models, we should either drop new features or drop old data when confronting feature incremental learning. By contrast, TransTab is able to continually learn from new data with incremental features. We split the raw dataset into three subsets: set1, 2, and 3 which mimic the incremental feature scenario shown by (2) in Fig. 1. Baseline methods apply to two scenarios: (a) learning from all data that only have features of set1 and (b) learning from the data of set3 only. We report the best of the two. TransTab applies to learning from all three subsets. Table 3 shows the results where we find our method outperforms baselines by a great margin. It demonstrates that TransTab makes the best of incremental features to learn better. Similar observations appear in public datasets, shown by Table 9. ",
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+    {
+        "type": "table",
+        "img_path": "images/692168404e8f12a32024ac3f23c610d769acfe0dbc49333305294d3a9b67b91a.jpg",
+        "table_caption": [
+            "Table 2: Test AUROC results on clinical trial mortality datasets the under supervised learning setting. All the remaining tables in this paper follow these setups to avoid clutter: the metric values are averaged over 10 random seeds; the Rank column reports the average rank across all datasets; Top results for each dataset are in bold. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>N00041119</td><td>N00174655</td><td>N00312208</td><td>N00079274</td><td>N00694382</td><td>Rank(Std)</td></tr><tr><td>LR</td><td>0.6364</td><td>0.8543</td><td>0.7382</td><td>0.7067</td><td>0.7360</td><td>5.40(1.14)</td></tr><tr><td>XGBoost</td><td>0.5937</td><td>0.5000</td><td>0.6911</td><td>0.6784</td><td>0.7440</td><td>9.60(3.71)</td></tr><tr><td>MLP</td><td>0.6340</td><td>0.6189</td><td>0.7427</td><td>0.6967</td><td>0.7063</td><td>8.00(2.83)</td></tr><tr><td>SNN</td><td>0.6335</td><td>0.9130</td><td>0.7469</td><td>0.6948</td><td>0.7246</td><td>5.80(2.39)</td></tr><tr><td>TabNet</td><td>0.5856</td><td>0.5401</td><td>0.6910</td><td>0.6031</td><td>0.7113</td><td>11.40(0.89)</td></tr><tr><td>DCN</td><td>0.6349</td><td>0.7577</td><td>0.7431</td><td>0.6952</td><td>0.7458</td><td>5.60(2.51)</td></tr><tr><td>AutoInt</td><td>0.6327</td><td>0.7502</td><td>0.7479</td><td>0.6958</td><td>0.7411</td><td>6.20(2.59)</td></tr><tr><td>TabTrans</td><td>0.6187</td><td>0.9035</td><td>0.7069</td><td>0.7178</td><td>0.7229</td><td>7.20(3.56)</td></tr><tr><td>FT-Trans</td><td>0.6372</td><td>0.9073</td><td>0.7586</td><td>0.7090</td><td>0.7231</td><td>4.20(2.28)</td></tr><tr><td>VIME</td><td>0.6397</td><td>0.8533</td><td>0.7227</td><td>0.6790</td><td>0.7232</td><td>7.00(3.08)</td></tr><tr><td>SCARF</td><td>0.6248</td><td>0.9310</td><td>0.7267</td><td>0.7176</td><td>0.7103</td><td>6.60(3.91)</td></tr><tr><td>TransTab</td><td>0.6408</td><td>0.9428</td><td>0.7770</td><td>0.7281</td><td>0.7648</td><td>1.00(0.00)</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/ddcfc85f989a4836432df34f7c981f094b816186702396dd3ae64bb459d177ba.jpg",
+        "table_caption": [
+            "Table 3: Test AUROC results on clinical trial datasets under feature incremental learning. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>N00041119</td><td>N00174655</td><td>N00312208</td><td>N00079274</td><td>N00694382</td><td>Rank(Std)</td></tr><tr><td>LR</td><td>0.6213</td><td>0.8485</td><td>0.6801</td><td>0.6258</td><td>0.7236</td><td>4.6(3.21)</td></tr><tr><td>XGBoost</td><td>0.5735</td><td>0.7890</td><td>0.6760</td><td>0.6038</td><td>0.6463</td><td>8.8(2.59)</td></tr><tr><td>MLP</td><td>0.6371</td><td>0.7754</td><td>0.6871</td><td>0.6220</td><td>0.6851</td><td>6.2(2.95)</td></tr><tr><td>SNN</td><td>0.5765</td><td>0.7440</td><td>0.6854</td><td>0.6336</td><td>0.7035</td><td>6.4(2.30)</td></tr><tr><td>TabNet</td><td>0.5548</td><td>0.8419</td><td>0.5849</td><td>0.6052</td><td>0.6668</td><td>9.0(3.39)</td></tr><tr><td>DCN</td><td>0.5172</td><td>0.5846</td><td>0.6640</td><td>0.6535</td><td>0.6957</td><td>8.2(4.16)</td></tr><tr><td>AutoInt</td><td>0.5232</td><td>0.6075</td><td>0.7031</td><td>0.6394</td><td>0.6974</td><td>7.2(3.56)</td></tr><tr><td>TabTrans</td><td>0.5599</td><td>0.7652</td><td>0.6433</td><td>0.6365</td><td>0.6841</td><td>8.2(1.10)</td></tr><tr><td>FT-Trans</td><td>0.5552</td><td>0.8045</td><td>0.7148</td><td>0.6471</td><td>0.6815</td><td>5.8(3.11)</td></tr><tr><td>VIME</td><td>0.6101</td><td>0.8114</td><td>0.3705</td><td>0.6444</td><td>0.6436</td><td>7.4(4.22)</td></tr><tr><td>SCARF</td><td>0.5996</td><td>0.6261</td><td>0.7072</td><td>0.6535</td><td>0.6957</td><td>5.2(2.97)</td></tr><tr><td>TransTab</td><td>0.6797</td><td>0.8545</td><td>0.7617</td><td>0.6857</td><td>0.7795</td><td>1.0(0.00)</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "3.3 Q3. Transfer learning ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "We further test if TransTab is able to transfer knowledge across tables. Results are in Table 4. We split each dataset into two subsets with $50 \\%$ overlaps of their columns. Baselines are trained and tested on set1 (only label-supervision) or set2 separately. For our method we pretrain it on set1 then finetune it on set2 and report its performance on set2, and vice versa. We observe that TransTab can benefit from knowledge transfer across tables to reach superior performances. Similar observations are made on public datasets shown by Table 10. ",
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+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 4: Test AUROC results on clinical trial datasets under transfer learning across tables. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">N00041119</td><td colspan=\"2\">NO0174655</td><td colspan=\"2\">N00312208</td><td colspan=\"2\">N00079274</td><td colspan=\"2\">N00694382</td><td rowspan=\"2\">Rank(Std)</td></tr><tr><td>set1</td><td>set2</td><td>set1</td><td>set2</td><td>set1</td><td>set2</td><td>set1</td><td>set2</td><td>set1</td><td>set2</td></tr><tr><td>LR</td><td>0.625</td><td>0.647</td><td>0.789</td><td>0.819</td><td>0.701</td><td>0.735</td><td>0.635</td><td>0.685</td><td>0.675</td><td>0.763</td><td>5.33(1.73)</td></tr><tr><td>XGBoost</td><td>0.638</td><td>0.575</td><td>0.574</td><td>0.886</td><td>0.690</td><td>0.700</td><td>0.596</td><td>0.647</td><td>0.592</td><td>0.677</td><td>7.56(3.75)</td></tr><tr><td>MLP</td><td>0.639</td><td>0.621</td><td>0.314</td><td>0.857</td><td>0.683</td><td>0.744</td><td>0.620</td><td>0.675</td><td>0.648</td><td>0.765</td><td>6.56(3.32)</td></tr><tr><td>SNN</td><td>0.627</td><td>0.634</td><td>0.215</td><td>0.754</td><td>0.687</td><td>0.732</td><td>0.631</td><td>0.683</td><td>0.651</td><td>0.759</td><td>7.44(2.07)</td></tr><tr><td>TabNet</td><td>0.564</td><td>0.558</td><td>0.856</td><td>0.592</td><td>0.671</td><td>0.657</td><td>0.443</td><td>0.605</td><td>0.581</td><td>0.677</td><td>10.67(2.96)</td></tr><tr><td>DCN</td><td>0.636</td><td>0.625</td><td>0.767</td><td>0.790</td><td>0.711</td><td>0.698</td><td>0.682</td><td>0.664</td><td>0.658</td><td>0.737</td><td>6.33(2.45)</td></tr><tr><td>AutoInt</td><td>0.629</td><td>0.630</td><td>0.843</td><td>0.730</td><td>0.725</td><td>0.698</td><td>0.679</td><td>0.665</td><td>0.686</td><td>0.661</td><td>5.89(2.89)</td></tr><tr><td>TabTrans</td><td>0.616</td><td>0.647</td><td>0.866</td><td>0.822</td><td>0.675</td><td>0.677</td><td>0.618</td><td>0.702</td><td>0.652</td><td>0.718</td><td>6.22(3.38)</td></tr><tr><td>FT-Trans</td><td>0.627</td><td>0.641</td><td>0.836</td><td>0.858</td><td>0.720</td><td>0.741</td><td>0.692</td><td>0.692</td><td>0.652</td><td>0.740</td><td>4.22(2.28)</td></tr><tr><td>VIME</td><td>0.603</td><td>0.625</td><td>0.312</td><td>0.726</td><td>0.601</td><td>0.642</td><td>0.477</td><td>0.668</td><td>0.614</td><td>0.715</td><td>10.44(1.51)</td></tr><tr><td>SCARF</td><td>0.635</td><td>0.657</td><td>0.651</td><td>0.814</td><td>0.653</td><td>0.686</td><td>0.682</td><td>0.701</td><td>0.671</td><td>0.776</td><td>5.56(3.40)</td></tr><tr><td>TransTab</td><td>0.653</td><td>0.653</td><td>0.904</td><td>0.846</td><td>0.730</td><td>0.756</td><td>0.680</td><td>0.711</td><td>0.747</td><td>0.774</td><td>1.78(1.30)</td></tr></table>",
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+        "table_caption": [
+            "Table 5: Test AUROC results on clinical trial datasets under zero-shot learning setting. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>TransTab</td><td>N00041119</td><td>N00174655</td><td>N00312208</td><td>N00079274</td><td>N00694382</td></tr><tr><td>Supervised</td><td>0.5854</td><td>0.6484</td><td>0.7536</td><td>0.7087</td><td>0.6479</td></tr><tr><td>Transfer</td><td>0.6130</td><td>0.6909</td><td>0.7658</td><td>0.7163</td><td>0.6752</td></tr><tr><td>Zero-shot</td><td>0.5990</td><td>0.6752</td><td>0.7576</td><td>0.7036</td><td>0.6740</td></tr></table>",
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+        "text": "3.4 Q4. Zero-shot learning ",
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+        "text": "Although there are numerous papers on zero-shot learning (ZSL) in CV and NLP [33, 34, 35], we notice that ZSL was hardly mentioned in tabular domain. In this experiment, we refer to the ZSL scenario mentioned by S(4) of Fig. 1 where we split the raw table into three equal-size subsets. Three subsets have distinct columns. For the zero-shot setting, the model learns from set1+set2 and is tested on set3 without further training. In this scenario, the model needs to leverage the learned knowledge from set1 and set2 to support the inference on a new table set3. Besides, we design two baselines for comparison: supervised where the model learns from set3 and predicts on set3 and transfer where the model learns from set1 $^ +$ set2 and continues to be finetuned on set3. Results are in Table 5. We surprisingly find the ZSL model gets better performance than the supervised one on average. It boils down to that (1) ZSL TransTab succeeds to retain the learned knowledge from set1+set2 for predicting on a new table (set3) and (2) ZSL can benefit from more data (set1 $^ +$ set2) than the supervised (set3 only). Meanwhile, the transfer model takes the advantage of set1 $^ +$ set2 and is adapted for set3 by finetuning, hence reaches the best performance. Similarly, we witness that TransTab is able to make zero-shot predictions on public datasets as in Table 11. ",
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+        "type": "text",
+        "text": "Additional sensitivity check is provided by Fig. 6 where we vary the overlap ratio of two subsets from the same dataset. We witness that our model makes reasonable predictions even if the training set has no column overlap with the test set. ",
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+        "type": "text",
+        "text": "3.5 Q5. Supervised and self-supervised pretraining ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We take experiments to compare the proposed VPCL with the vanilla transfer learning strategy, as in Table 6. We observe that the vanilla strategy harms the performance on two datasets while VPCL always brings positive effect for finetuning. Besides, we conduct experiments on varying the number of partitions and show the average AUROC on all five datasets, shown by Fig. 4. We specify that VPCL demonstrates an advantage over self-VPCL when we increase the partition numbers. ",
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+        "type": "text",
+        "text": "We also explore if pretraining works on public datasets. Results in Table 12 somewhat match our expectations that pretraining on unrelated tabular data usually yields few benefits for finetuning because these tables define totally different columns and targeted tasks. We also show the ablation on the number of partitions by Fig. 5 where VPCL consistently outperforms the Supervised baseline. ",
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+        "type": "table",
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+        "table_caption": [
+            "Table 6: Test AUROC on clinical trial datasets under the across-table pretraining plus finetuning setting. Supervised: baseline supervised model; Transfer: vanilla supervised transfer learning. Red shows the one worse than the Supervised baseline. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>TransTab</td><td>N00041119</td><td>N00174655</td><td>NO0312208</td><td>NO0079274</td><td>N00694382</td></tr><tr><td>Supervised</td><td>0.6313</td><td>0.8348</td><td>0.7444</td><td>0.6885</td><td>0.7293</td></tr><tr><td>Transfer</td><td>0.6424</td><td>0.8183</td><td>0.7458</td><td>0.6928</td><td>0.7239</td></tr><tr><td>Self-VPCL</td><td>0.6412</td><td>0.8577</td><td>0.7486</td><td>0.7069</td><td>0.7348</td></tr><tr><td>VPCL</td><td>0.6405</td><td>0.8583</td><td>0.7517</td><td>0.7063</td><td>0.7392</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "Nevertheless, it is still worth investigating the table phenotypes to aggregate tables which are more likely to benefit from each other by transfer learning. ",
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+    {
+        "type": "text",
+        "text": "4 Related Works ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Tabular Prediction. To enhance tabular predictions, numerous recent works try to design new algorithms [28, 36, 37, 30, 38, 32, 5, 10, 7, 39, 40, 41, 42, 43, 44, 45]. However, it was argued that boosting algorithms and MLPs are still the competitive choices for tabular data modeling, especially when the sample size is small [32, 46, 39, 47]. To alleviate label scarcity issue, SSL pretraining on unlabeled tabular data was introduced [2, 24, 10, 9, 11]. Nonetheless, none of them is transferable across tables then is able to extend the success of pretraining to the tabular domain. For practical tabular predictions, the common case is that we own a lot of labeled samples collected with diverse protocols hence heavy preprocessing is needed to align them by either dropping many samples or many features. By contrast, TransTab accepts variable-column tables and therefore can learn from different tables at scale and transfer to the target task. Also, it can support diverse tabular prediction tasks as depicted in Fig. 1, which cannot be done by off-the-shelf tabular methods. ",
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+    {
+        "type": "text",
+        "text": "Transfer learning. Transfer learning (TL) has long been a popular research field since the proposal of ImageNet [48], which gives rise to splendid works on utilizing supervised pretraining on a large general database and finetune on a small downstream task [49, 50, 51, 52, 53]. TL is also fast-growing in NLP beginning at BERT [20], which often leverages web-scale unlabeled texts for self-supervised pretraining and then applies to specific tasks [34, 54, 55, 56, 57]. However, few work was on TL in tabular predictions. As mentioned in $\\ S$ , TransTab paves the way for effective tabular TL by establishing a feature processing protocol that applies for most table inputs, such that it shares knowledge across tables. ",
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+    {
+        "type": "text",
+        "text": "Self-supervised learning & contrastive learning. SSL uses unlabeled data with pretext tasks to learn useful representations and most of them are in CV and NLP [20, 17, 15, 16, 58, 23, 59, 60, 61, 62, 63]. Recent SSL tabular models can be classified into reconstruction and contrastive based methods: TabNet [30] and VIME [2] try to recover the corrupted inputs with auto-encoding loss; SCARF [11] takes a SimCLR-like [64] contrastive loss between the sample and its corrupted version; SubTab [9] takes a combination of both. Nevertheless, all fail to learn transferable models across tables such that cannot benefit from pretraining with scale. Contrastive learning can also be applied to supervised learning by leveraging class labels to build positive samples [26]. Our work extends it to to the tabular domain, which we prove works better than vanilla supervised pretraining. The vertical partition sampling also enjoys high query speed from large databases which are often column-oriented [25]. Another line of research takes table pretraining table semantic parsing [65, 66, 67, 68, 69] or table-to-text generation [70, 71]. But these methods either encode the whole table instead of each row or do not demonstrate to benefit tabular prediction yet. ",
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+    {
+        "type": "text",
+        "text": "5 Conclusion ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This paper proposes TransTab that accepts variable-column inputs. By the proposed vertical partition contrastive learning, it can benefit from supervised pretraining from multiple tabular datasets with low memory cost. We envision it to be the basis of tabular foundation models and widely used to tabular-related applications in the future. ",
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+    {
+        "type": "text",
+        "text": "Acknowledgement ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "This work was supported by NSF award SCH-2205289, SCH-2014438, IIS-1838042, NIH award R01 1R01NS107291-01. ",
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+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
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+    },
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+        "type": "text",
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In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics, pages 528–537, 2022.   \n[70] Fei Wang, Kexuan Sun, Muhao Chen, Jay Pujara, and Pedro A Szekely. Retrieving complex tables with multi-granular graph representation learning. In SIGIR, 2021.   \n[71] Fei Wang, Zhewei Xu, Pedro Szekely, and Muhao Chen. Robust (controlled) table-to-text generation with structure-aware equivariance learning. arXiv preprint arXiv:2205.03972, 2022.   \n[72] Vincenzo Cutrona. Semantic enrichment for large-scale data analytics. 2019.   \n[73] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library. Advances in Neural Information Processing Systems, 32, 2019.   \n[74] Aaron Van den Oord, Yazhe Li, Oriol Vinyals, et al. 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parse/dev/AOKU4nRw1W/AOKU4nRw1W.md

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+# Linguistic Binding in Diffusion Models: Enhancing Attribute Correspondence through Attention Map Alignment
+
+Royi Rassin Bar-Ilan University, Israel rassinroyi@gmail.com
+
+Eran Hirsch Bar-Ilan University, Israel eran.hirsch@biu.ac.il
+
+Daniel Glickman Bar-Ilan University, Israel danielglickman1@gmail.com
+
+# Shauli Ravfogel
+
+Bar-Ilan University, Israel Allen Institute for AI, Israel shauli.ravfogel@gmail.com
+
+Yoav Goldberg Bar-Ilan University, Israel Allen Institute for AI, Israel yoav.goldberg@gmail.com
+
+Gal Chechik   
+Bar-Ilan University, Israel NVIDIA, Israel   
+gal.chechik@biu.ac.il
+
+# Abstract
+
+Text-conditioned image generation models often generate incorrect associations between entities and their visual attributes. This reflects an impaired mapping between linguistic binding of entities and modifiers in the prompt and visual binding of the corresponding elements in the generated image. As one example, a query like “a pink sunflower and a yellow flamingo” may incorrectly produce an image of a yellow sunflower and a pink flamingo. To remedy this issue, we propose SynGen, an approach which first syntactically analyses the prompt to identify entities and their modifiers, and then uses a novel loss function that encourages the cross-attention maps to agree with the linguistic binding reflected by the syntax. Specifically, we encourage large overlap between attention maps of entities and their modifiers, and small overlap with other entities and modifier words. The loss is optimized during inference, without retraining or fine-tuning the model. Human evaluation on three datasets, including one new and challenging set, demonstrate significant improvements of SynGen compared with current state of the art methods. This work highlights how making use of sentence structure during inference can efficiently and substantially improve the faithfulness of text-to-image generation.1
+
+# 1 Introduction
+
+Diffusion models for text-conditioned image generation produce impressive realistic images [1, 2, 3, 4]. Users control the generated content through natural-language text prompts that can be rich and complex. Unfortunately, in many cases the generated images are not faithful to the text prompt [5, 6]. Specifically, one very common failure mode results from improper binding, where modifier words fail to influence the visual attributes of the entity-nouns to which they are grammatically related.
+
+![](images/264729368610ffdc703d68a9e741608fdad401d8cca9c4849a3a393a1ee40540.jpg)  
+Figure 1: Visual bindings of objects and their attributes may fail to match the linguistic bindings between entities and their modifiers. Our approach, SynGen, corrects these errors by matching the cross-attention maps of entities and their modifiers.
+
+As an illustration, consider the prompt “a pink sunflower and a yellow flamingo”. Given this prompt, current models often confuse the modifiers of the two entity-nouns, and generate an image of a yellow sunflower and a pink flamingo (Fig. 1, bottom left, semantic leak in prompt). In other cases, the attribute may semantically leak to areas in the image that are not even mentioned in the prompt (Fig. 1, bottom center, semantic leak outside prompt) or the attribute may be completely neglected and missed from the generated image (Fig. 1, bottom right, attribute neglect). Such mismatch can be addressed by providing non-textual control like visual examples [7, 8], but the problem of correctly controlling generated images using text remains open.
+
+A possible reason for these failures is that diffusion models use text encoders like CLIP [9], which are known to fail to encode linguistic structures [10]. This makes the diffusion process “blind" to the linguistic bindings, and as a result, generate objects that do not match their attributes. Building on this intuition, we propose to make the generation process aware of the linguistic structure of the prompt. Specifically, we suggest to intervene with the generation process by steering the cross-attention maps of the diffusion model. These cross-attention map serve as a link between prompt terms and the set of image pixels that correspond to these terms. Our linguistics-based approach therefore aims to generate an image where the visual binding between objects and their visual attributes adheres to the syntactic binding between entity-nouns and their modifiers in the prompt.
+
+Several previous work devised solutions to improve the relations between prompt terms and visual components, with some success [11, 12, 13]. They did not focus on the problem of modifier-entity binding. Our approach specifically addresses this issue, by constructing a novel loss function that quantifies the distance between the attention patterns of grammatically-related (modifier, entity-noun) pairs, and the distance between pairs of unrelated words in the prompt. We then optimize the latent denoised image in the direction that separates the attention map of a given modifier from unrelated tokens and bring it closer to its grammatically-related noun. We show that by intervening in the latent code, we markedly improve the pairing between attributes and objects in the generated image while at the same time not compromising the quality of the generated image.
+
+We evaluate our method on three datasets. (1) For a natural-language setting, we use the natural compositional prompts in the ABC-6K benchmark [13]; (2) To provide direct comparison with previous state-of-the-art in [11], we replicate prompts from their setting; (3) Finally, to evaluate binding in a challenging setting, we design a set of prompts that includes a variety of modifiers and entity-nouns. On all datasets, we find that SynGen shows significant improvement in performance based on human evaluation, sometimes doubling the accuracy. Overall, our work highlights the effectiveness of incorporating linguistic information into text-conditioned image generation models and demonstrates a promising direction for future research in this area.
+
+(a) Entity-Modifier Identification
+
+![](images/4807e34e96c095ba2f7869333df66481bf77d71d1bb38753edfe5bb3fed126e0.jpg)  
+Figure 2: The SynGen workflow and architecture. (a) The text prompt is analyzed to extract entitynouns and their modifiers. (b) SynGen adds intermediates steps to the diffusion denoising process. In that step, we update the latent representation to minimize a loss over the cross attention maps of entity-nouns and their modifiers (Eq 3).
+
+The main contributions of this paper are as follows: (1) A novel method to enrich the diffusion process with syntactic information, using inference-time optimization with a loss over cross-attention maps; (2) A new challenge set of prompts containing a rich number and types of modifiers and entities.
+
+# 2 Syntax-Guided Generation
+
+Our approach, which we call SynGen, builds on two key ideas. First, it is easy to analyze the syntactic structure of natural language prompts to identify bindings of entity-nouns and their modifiers. Second, one can steer the generation of images to adhere to these bindings by designing an appropriate loss over the cross-attention maps of the diffusion model. We describe the two steps of our approach: extracting syntactic bindings and then using them to control generation.
+
+# 2.1 Identifying entity-nouns and their modifiers
+
+To identify entity-nouns and their corresponding modifiers, we traverse the syntactic dependency graph, which defines the syntactic relation between words in the sentence. Concretely, we parse the prompt using spaCy’s transformer-based dependency parser [14] and identify all entity-nouns (either proper-nouns or common-nouns) that are not serving as direct modifiers of other nouns.
+
+These are the nouns that correspond to objects in the generated image. We then recursively collect all modifiers2 of the noun into its modifier set. The set of modifier-labels includes a range of syntactic relations between nouns and their modifiers, such adjectivial modification (amod; “the regal dog”), compounds (compound; “the treasure map”), nominal modification through an intervening marker, adverbial modifiers (npadvmod; “A watermelon-styled chair”), adjectivial complement (acomp; “The apple is blue”), and coordination between modifiers (conj; “A black and white dog”).
+
+# 2.2 Controlling generation with language-driven cross-attention losses
+
+Consider a pair of a noun and its modifier. We expect the cross-attention map of the modifier to largely overlap with the cross-attention map of the noun, while remaining largely disjoint with the maps corresponding to other nouns and modifiers. To encourage the denoising process to obey these spatial relations between the attention maps, we design a loss that operates on all cross-attention maps. We then use this loss with a pretrained diffusion model during inference. Specifically, we
+
+![](images/7f6875d2c4e2d0b6c4e204cba6270ae9115ffcc35a00751ed7b4f8ff125294fd.jpg)  
+Figure 3: Evolution of cross-attention maps and latent representation along denoising steps, for the prompt “a red crown and a golden strawberry”. At first, the attention maps of all modifiers and entity-nouns are intertwined, regardless of the expected binding. During denoising, attention maps gradually becomes separated, adhering the syntactic bindings. The vertical line indicates that after 25 steps intervention stops, but the attention maps remain separated.
+
+optimize the noised latents by taking a gradient step to reduce that loss. See illustration in Fig. 2.   
+Fig. 3 illustrates the effect of the loss over the cross-attention maps.
+
+Loss functions: Consider a text prompt with $N$ tokens, for which our analysis extracted $k$ nounmodifier sets $\{ S _ { 1 } , S _ { 2 } , \ldots , S _ { k } \}$ . Let $P ( S _ { i } )$ represent all pairs $( m , n )$ of tokens between the noun root $n$ and its modifier descendants $m$ in the $i$ -th set $S _ { i }$ . For illustration, the set of “A black striped dog” contains two pairs (“black”, “dog”) and (“striped”, “dog”). Next, denote by $\{ A _ { 1 } , A _ { 2 } , \dotsc , { \overline { { A _ { N } } } } \}$ the attention maps of all $N$ tokens in the prompt, and denote by $d i s t ( A _ { m } , A _ { n } )$ a measure of distance (lack of overlap) between attention maps $A _ { m }$ and $A _ { n }$ .
+
+Our first loss aims to minimize that distance (maximize the overlap) over all pairs of modifiers and their corresponding entity-nouns $( m , n )$ ,
+
+$$
+\mathcal { L } _ { p o s } ( A , S ) = \sum _ { i = 1 } ^ { k } \sum _ { ( m , n ) \in P ( S _ { i } ) } d i s t ( A _ { m } , A _ { n } ) .
+$$
+
+We also construct a loss that compares pairs of modifiers and entity-nouns with the remaining words in the prompt, which are grammatically unrelated to these pairs. In other words, this loss is defined between words within the (modifiers, entity-nouns) set and words outside of it. Formally, let $U ( S _ { i } )$ represent the set of unmatched words obtained by excluding the words in $S _ { i }$ from the full set of words and $A _ { u }$ is the corresponding attention map for a given unrelated word $u$ . The following loss encourages moving apart grammatically-unrealted pairs of words:
+
+$$
+\mathcal { L } _ { n e g } = - \sum _ { i = 1 } ^ { k } \frac { 1 } { | U ( S _ { i } ) | } \sum _ { ( m , n ) \in P ( S _ { i } ) } \sum _ { u \in U ( S _ { i } ) } \frac { 1 } { 2 } \bigg ( d i s t ( A _ { m } , A _ { u } ) + d i s t ( A _ { u } , A _ { n } ) \bigg ) .
+$$
+
+Our final loss combines the two loss terms:
+
+$$
+\begin{array} { r } { \mathcal { L } = \mathcal { L } _ { p o s } + \mathcal { L } _ { n e g } . } \end{array}
+$$
+
+For a measure of distance between attention maps we use a symmetric Kullback-Leibler divergence $\begin{array} { r } { d i s t ( A _ { i } , A _ { j } ) = \frac { 1 } { 2 } D _ { K L } ( A _ { i } | | A _ { j } ) + \frac { 1 } { 2 } D _ { K L } ( A _ { j } | | \mathcal { \bar { A } } _ { i } ) } \end{array}$ , where $A _ { i }$ , $A _ { j }$ are attention maps normalized to a sum of 1, $i$ and $j$ are generic indices, and $\begin{array} { r } { \dot { D _ { K L } } ( A _ { i } | | A _ { j } ) = \sum _ { p i x e l s } A _ { i } \log ( A _ { i } / A _ { j } ) } \end{array}$ .
+
+Our test-time optimization approach resembles the one of [11], which defined a loss over the crossattention maps to update the latents at generation time. However, their loss aims to maximize the presence of the smallest attention map at a given timestep to guarantee a set of selected tokens is included in the generated image, and our loss depends on pairwise relations of linguistically-related words and aims to align the diffusion process to the linguistic-structure of the prompt.
+
+# 2.3 The workflow
+
+We use the loss of Eqs 1-3 to intervene in the first 25 out of 50 denoising steps. Empirically, using a smaller number of steps did not correct well improper binding, and using a larger number generated blurred images, as detailed in Appendix B. In each of the first 25 steps, a pretrained denoiser (U-Net) was first used to denoise the latent variable $z _ { t }$ . Then, we obtained the cross-attention maps as in [15]. Next, we used the loss $\mathcal { L }$ to update the latent representation $z _ { t }$ with a gradient step $z _ { t } ^ { \prime } = z _ { t } - \alpha \cdot \nabla _ { z _ { t } } \mathcal { L }$ . Finally, the U-Net architecture denoises the updated latent variable $z _ { t } ^ { \prime }$ for the next timestep.
+
+# 3 Experiments
+
+# 3.1 Compared baseline methods
+
+We compare SynGen with three baseline methods. (1) Stable Diffusion 1.4 (SD) [1]; (2) Structured Diffusion [13], extracts noun-phrases from the prompt and embeds them separately, to improve the mapping of the semantics in the cross-attention maps; and (3) Attend-and-Excite (A&E) [11], a method that given a predetermined set of tokens, updates the latent a certain number of timesteps, to eventually incorporate these tokens in the generated image. To automate token selection in A&E, we follow the recommendation by the authors to select the nouns using a part-of-speech tagger.
+
+# 3.2 Datasets
+
+We evaluate our approach using two existing benchmark datasets, and one new dataset that we designed to challenge methods in this area.
+
+(1) ABC-6K [13]. This benchmark consists of 3.2K natural compositional prompts from MSCOCO [16], which were manually written by humans, using natural language and contain at least two color words modifying different noun-entities. In addition, the dataset contains 3.2K counterparts, where the position of modifiers in the original prompts are swapped. (e.g., “a white bench in front of a green bush” and “a green bench in front of a white bush”). We randomly sample 600 prompts.
+
+(2) Data from Attend-and-Excite [11]. Originally introduced to evaluate the A&E method which focuses on entity-neglect, this dataset also showed that A&E improved over previous work in terms of improper binding.
+
+Prompts in this dataset belong to three categories: (1) “a {color} {in-animate object} and a {color} {in-animate object}”; (2) “a {color} {in-animate object} and an {animal}”; (3) “an {animal} and an {animal}”. Following the split in A&E, we sample 33 prompts from type (1) and 144 prompts from type (2), but exclude type (3), as it does not contain modifiers. This is a very simple dataset, which we use to facilitate direct comparison with previous work.
+
+(3) Diverse Visual Modifier Prompts (DVMP). The above two datasets are limited in terms of number and types of modifiers, and the number of entity-nouns per prompt. To challenge our model, we design a dataset consisting of coordination sentences, in similar fashion to the dataset from A&E, but with strong emphasis on the number and types of modifiers per prompt. Specifically, we aim to compare the models with prompts that contain numerous and uncommon modifiers, creating sentences that would not usually be found in natural language or training data, such as “a pink spotted panda”. DVMP was designed with two key aspects in mind:
+
+Expanding the set of modifiers: We have extended the number of modifiers referring to an entitynoun from one to up to three. For instance, “a blue furry spotted bird”. We also added types of modifiers besides colors, including material patterns (“a metal chair”), design patterns (“a checkered shoe”), and even nouns modifying other noun-entities (“a baby zebra”).
+
+Visually verifiable and semantically coherent: The modifiers selected for DVMP are visually verifiable, with a deliberate avoidance of nuanced modifiers. For instance, “big” is a relative modifier dependent on its spatial context, and emotional states, such as in the prompt “an excited dog”, are largely excluded due to their subjective visual interpretation. Simultaneously, DVMP maintains semantic coherence by appropriately matching modifiers to noun-entities, thereby preventing the creation of nonsensical prompts like “a sliced bowl” or “a curved zebra”.
+
+In total, we have generated 600 prompts through random sampling. For a comprehensive description of the dataset’s creation, see Appendix F.
+
+# 3.3 Human Evaluation
+
+We evaluate image quality using Amazon Mechanical Turk (AMT). Raters were provided with a multiple-choice task, consisting of a single text prompt and four images, each generated by the baselines and SynGen. Raters could also indicate that all images are “equally good” or “equally bad”. We provided each prompt and its corresponding generations to three raters, and report the majority decision. In cases where there is no majority model winner, we count it toward “no majority winner”.
+
+We evaluate generated images in two main aspects: (1) concept separation (sometimes known as editability [17]) and (2) visual appeal. Concept separation refers to the ability of the model to distinctly depict different concepts or objects in the generated image. The effectiveness of concept separation is assessed by asking raters, “Which image best matches the given description?”. To asses visual quality, raters were asked “Which image is more visually appealing?”. To maintain fairness and reduce biases, the order of images was randomized in each task. Full rater instructions and further details are provided in Appendix G.1 of the supplemental materials.
+
+We also experimented automatic evaluation, but find its quality subpar. For standardized evaluation purposes, it is detailed in Appendix G.2.
+
+Fine-grained evaluation. In addition to a multiple-choice task, we evaluate concept separation using the following key metrics: (1) Proper Binding, quantifying how well the model associates attributes with their corresponding objects; (2) Improper Binding, measuring the instances where attributes are incorrectly linked to unrelated objects; and (3) Entity Neglect, capturing the frequency with which the model omits entities specified in the prompt.
+
+To this end, we randomly select 200 prompts each from the DVMP and ABC-6K datasets, while using all 177 prompts available in the A&E dataset. Human evaluators were asked to mark if instances have correct or incorrect attribute-object mapping. Importantly, incorrect mappings are counted on a per-attribute basis—multiple incorrect mappings of a single attribute are considered one violation. For example, in the prompt “the white dog chased the cat up the tree”, if the modifier “white” is incorrectly mapped to both “cat” and “tree”, it is counted as one instance of violation. Evaluators also identify the number of entities mentioned in the prompt that are subsequently depicted in the generated image.
+
+Based on these counts, we define the metric of Proper Binding as the ratio of correctly mapped attributes to the total number of attributes. Similarly, Improper Binding is defined as the ratio of incorrectly mapped attributes to the total number of attributes, while Entity Neglect is the complement of the ratio of mentioned entities that are depicted in the generated image to the total number of entities in the prompt. Rater instructions are provided in Appendix G.1.
+
+# 4 Results
+
+# 4.1 Quantitative Results
+
+Table 1 provides results of the comparative experiment. SynGen is consistently ranked first in all three datasets, and by a large margin, sometimes double the approval rate of the second ranked method, A&E. These results are observed for concept separation, which measures directly the semantic leak, and for visual appeal.
+
+The high number of “no winner” cases reflects the large difficulty of some of the prompts, for which no method provides good enough generated images. Population results before majority aggregation are given in Appendix G.1 of the supplemental material. Comparisons with StableDiffusion are given in Fig. 19 of the supplemental.
+
+Table 2 provides results of the individual experiment. We find that SynGen outperforms all models by a landslide in both proper and improper binding and is on par with state-of-the-art on entity neglect [11], despite not directly tackling this problem.
+
+Table 1: Human evaluation of all methods on the three datasets. The table reports scores for concept separation (how well the image matches the prompt) and visual appeal. Values are the fraction of majority vote of three raters, normalized to sum to 100.   
+
+<table><tr><td colspan="2"></td><td colspan="2">Concept Visual Separation Appeal</td></tr><tr><td>Dataset</td><td>Model</td><td>38.42</td><td>37.85</td></tr><tr><td rowspan="4">A&amp;E</td><td>SynGen (ours) A&amp;E</td><td>18.08</td><td>18.65</td></tr><tr><td>Structured Diffusion</td><td>04.52</td><td>04.52</td></tr><tr><td>Stable Diffusion</td><td>01.69</td><td>02.26</td></tr><tr><td>No majority winner</td><td>37.29</td><td>36.72</td></tr><tr><td rowspan="5">DVMP (challenge set)</td><td>SynGen (ours)</td><td>24.84</td><td>16.00</td></tr><tr><td>A&amp;E</td><td>13.33</td><td>12.17</td></tr><tr><td>Structured Diffusion</td><td>04.33</td><td>07.83</td></tr><tr><td>Stable Diffusion</td><td>03.83</td><td>07.17</td></tr><tr><td> No majority winner</td><td>53.67</td><td>56.83</td></tr><tr><td rowspan="5">ABC-6K</td><td>SynGen (ours)</td><td>28.00</td><td>18.34</td></tr><tr><td>A&amp;E</td><td>11.17</td><td>10.00</td></tr><tr><td>Structured Diffusion</td><td>05.83</td><td>06.33</td></tr><tr><td>Stable Diffusion</td><td>04.83</td><td>07.83</td></tr><tr><td>No majority winner</td><td>50.17</td><td>57.50</td></tr></table>
+
+Table 2: Results of the fine-grained concept separation experiment. Proper Binding should be maximized to 100, while Improper Binding and Entity Neglect should be minimized to 0.   
+
+<table><tr><td colspan="4">Proper Binding ↑Improper Binding↓Entity Neglect↓</td></tr><tr><td>Dataset</td><td>Model</td><td>94.76</td><td>23.81 02.82</td></tr><tr><td rowspan="4">A&amp;E</td><td>SynGen (ours) A&amp;E</td><td>81.90</td><td>63.81 01.41</td></tr><tr><td>Structured Diffusion</td><td>55.71</td><td>67.62 21.13</td></tr><tr><td>Stable Diffusion</td><td>59.05</td><td>68.57 20.56</td></tr><tr><td></td><td></td><td>16.26</td></tr><tr><td rowspan="4">DVMP</td><td>SynGen (ours) A&amp;E</td><td>74.90 52.47</td><td>19.49 31.64</td></tr><tr><td>(challenge set) Structured Diffusion</td><td>48.73</td><td>10.77 30.57 28.46</td></tr><tr><td>Stable Diffusion</td><td>47.80</td><td>30.44</td></tr><tr><td></td><td></td><td>26.22</td></tr><tr><td rowspan="4">ABC-6K</td><td>SynGen (ours)</td><td>63.68</td><td>14.37 34.41</td></tr><tr><td>A&amp;E</td><td>56.26</td><td>26.43 33.18</td></tr><tr><td>Structured Diffusion</td><td>51.47</td><td>29.52 34.57</td></tr><tr><td>Stable Diffusion</td><td>52.70</td><td>27.20 36.57</td></tr></table>
+
+# 4.2 Qualitative Analysis
+
+Figures 4–6 provide qualitative examples from the three datasets, comparing SynGen with the two strongest baselines.
+
+The qualitative examples illustrate several failure modes of our baselines. First, semantic leak in prompt, occurs when a modifier of an entity-noun “leaks” onto a different entity-noun in the prompt, as shown in Fig. 4, for the prompt “a pink clock and a brown chair”, in columns 3 and 4. In this case, all baselines incorrectly apply pink hues to the chair, despite the prompt explicitly defining it as brown. A more nuanced variant of this issue is semantic leak out of prompt, when a modifier is assigned to an entity-noun that is not mentioned in the prompt. For instance, the “spiky” attribute in “a spiky bowl and a green cat” leaks to a plant, which is not in the prompt, or the green coloration in the background of the images generated by the baselines, as seen in columns 5 and 6 in Fig. 5.
+
+Attribute neglect occurs when a modifier from the prompt is absent from the generated image. As exhibited in Fig. 4, for “a frog and a brown apple”, both baselines do not include a brown color at all.
+
+Entity casting is another failure type where a modifier is treated as a standalone entity, a phenomenon commonly observed with noun modifiers. For example, the prompt “a wooden crown and a furry baby
+
+“a monkey and a black bow”
+
+“a pink clock and a brown chair”
+
+“a frog and a brown apple”
+
+![](images/a777c9e743a8743bd48c52375b3605b8d075c22102b51e2eb94e44626edee5ab.jpg)  
+Figure 4: Qualitative comparison for prompts from the Attend-and-Excite dataset. For every prompt, the same three seeds are used for all methods.
+
+![](images/3d2dc4c397649e36926c46fb04f63eb696043784f014c5d6044403a0ba644ed9.jpg)  
+Figure 5: Qualitative comparison for prompts from the DVMP dataset. For every prompt, the same three seeds are used for all methods.
+
+rabbit” (column 1 in Fig. 5) has all methods, apart from ours, generate human infants. Presumably, this occurs because “baby” is interpreted as a noun rather than as a modifier, leading other methods to treat it as a separate object due to the lack of syntactic context. Conversely, SynGen correctly interprets “baby” as a modifier and accurately binds it to the rabbit. Similarly, in the prompt “a white fire hydrant sitting in a field next to a red building” (column 6 in Fig. 6), “fire” is wrongly interpreted as an entity-noun, which leads to the unwarranted inclusion of a fire in the scene.
+
+All methods, barring SynGen, grapple with entity entanglement [18, 19, 20, 21, 22], where some objects tend to strongly associate with their most common attribute (e.g., tomatoes are typically red). This is evident in columns 3 and 4 in Fig. 6, where other methods fail to visually associate the blue attribute with the dog in “a blue and white dog sleeps in front of a black door”. Instead, they resort to typical attributes of the objects, generating a black and white dog.
+
+Further qualitative analysis is provided in Appendix D.1.
+
+![](images/486e4fc4a5cd44205d7a513efd3d0d97a278708b573547004a513281466aa667.jpg)  
+Figure 6: Qualitative examples for ABC-6K prompts. For every prompt, all methods use the same three seeds.
+
+# 4.3 Ablation study
+
+The importance of using both positive and negative losses. We evaluated the relative importance of the two terms in our loss Eq. (3). The positive term $\mathcal { L } _ { p o s }$ , which encourages alignment of the attention map of an object and its modifiers, and the negative loss term, $\mathcal { L } _ { n e g }$ , which discourages alignment with other modifiers and objects. We sampled 100 prompts from the DVMP dataset and generated images with and without each of the two loss terms. See example in Fig. 7. Then, raters were asked to select the best of four variants. Table 3 shows that raters preferred the variant that combined both the positive and the negative terms. More examples are given in the supplemental Appendix B.
+
+Table 3: Ablation of loss components. Values are percent preferred by human raters.   
+
+<table><tr><td>Loss</td><td>Concept Separation</td><td>Visual Appeal</td></tr><tr><td>Both losses Lpos +Lneg</td><td>27</td><td>22</td></tr><tr><td>Positive only Lpos</td><td>0</td><td>11</td></tr><tr><td>Negative only Lneg</td><td>3</td><td>35</td></tr><tr><td>Stable Diffusion</td><td>4</td><td>28</td></tr><tr><td>No majority winner</td><td>66</td><td>4</td></tr></table>
+
+![](images/e3c165622fa35e95824edd899ab51ef0684b7f2be54a379401c59348371bd3ec.jpg)  
+Figure 7: Ablation of loss components. Removing $\mathcal { L } _ { n e g }$ results in semantic leakage (the bird is white) and entity neglect (there is no crown). Removing $\mathcal { L } _ { p o s }$ also leads to semantic leakage (generating a bird and background with white parts), and failed attribution binding (generating a crown that is not white).
+
+# 5 Related Work
+
+Semantic leakage. [2] pointed out cases of semantic leakage in diffusion models, where properties of one entity-noun influence the depiction of another. [23] attributed this issue to a lack of understanding of syntax, specifically noting failures when processing texts requiring subtle syntactic binding comprehension. [6] identified semantic leakage issues in DALL-E, where properties of one entitynoun influence how other entity nouns are depicted. In this work, we pinpoint semantic leakage as a consequence of improper mapping between syntactic and visual binding.
+
+Attention-based interventions. [15] demonstrated that the cross-attention mechanism determines the spatial layout of entities in generated images. This result suggested that cross-attention is causally involved in the aforementioned issues. A&E [11] addresses the problem of entity omission, where certain entities mentioned in the prompt do not appear in the generated image. They propose a loss function that encourages each noun token in the image to significantly attend to a corresponding image patch, thereby preventing its omission. Our approach is similar to [11] in that it updates the latent representation through a loss function over attention maps, during image generation.
+
+Syntax-based generation was also explored in [13], proposing the Structured Diffusion method. It aims to address the problem of missing entities and semantic leakage of attributes. This is achieved by parsing the prompt, extracting phrases corresponding to nouns and modifiers, and encoding them separately. They also intervene in the attention patterns, ensuring that each individual phrase influences the attention patterns. Our experiments show that it is better to implicitly influence the attention patterns through our loss which we dynamically optimize. In contrast, their intervention remains fixed.
+
+Concurrent to this work, [24] proposed an alternative approach to combine syntactic control and attention-based optimization. They extract nouns from prompts and train a layout predictor to identify the corresponding pixels for each noun. Then, they optimize the latents by encouraging the pixels corresponding to the objects to attend to CLIP representations of phrases containing those objects. While similar in spirit, the current paper demonstrates intervention in the generation process solely based on syntax, without explicitly learning the correspondence between image entities and tokens.
+
+# 6 Limitations
+
+Like previous methods, the performance of SynGen degrades with the number of attributes to be depicted (see supplemental Fig. 12). However, its decline is remarkably less pronounced compared to other methods. This decay in performance can be attributed to two primary factors: (1) an image begins to lose its visual appeal when the negative loss term becomes excessively large; (2) an overly cluttered image poses challenges in crafting a cohesive “narrative” for all the concepts. We expect that some of these issues can be addressed with more hyper-parameter tuning.
+
+Naturally, the effectiveness of our method is intrinsically tied to the quality of the parser. When the parser fails to extract the stipulated syntactic relations, our method essentially operates akin to SD.
+
+Finally, SynGen takes longer to generate images with modifiers in the prompt than SD and slightly slower than than A&E (see Appendix A).
+
+# 7 Conclusions
+
+In this work, we target the improper binding problem, a common failure mode of text-conditioned diffusion models, where objects and their attributes incorrectly correspond to the entity-nouns and their modifiers in the prompt. To address it, we propose SynGen, an inference-time intervention method, with a loss function that encourages syntax-related modifiers and entity-nouns to have overlapping cross-attention maps, and discourages an overlap from cross-attention maps of other words in the prompt. We challenge our method with three datasets, including DVMP – a new dataset that is specially-designed to draw out hard cases of improper-binding problem. Our method demonstrates improvement of over $100 \%$ across all three datasets over the previous state-of-the-art. Finally, our work highlights the importance of linguistic structure during denoising for attaining faithful text-to-image generation, suggesting promising avenues for future research.
+
+# Acknowledgements
+
+This study was funded by a grant to GC from the Israel Science Foundation (ISF 737/2018) and an equipment grant to GC and Bar-Ilan University from the Israel Science Foundation (ISF 2332/18). This project has also received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant agreement No. 802774 (iEXTRACT). Shauli Ravfogel is grateful to be supported by the Bloomberg Data Science PhD Fellowship.
+
+References   
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+
+# Supplementary Material
+
+# A Implementation Details
+
+Computing resources. Experiments were run on an NVIDIA DGX Station with four v100-SXM2- 32GB GPUs. The overall duration of all experiments in the paper was about two weeks.
+
+Efficiency. SynGen takes ${ \sim } 1 4 4 \%$ longer than SD and ${ \sim } 1 0 . 9 \%$ longer than A&E to generate images with modifiers in the prompt. To arrive to these numbers, we randomly sampled a set of 50 images from the A&E dataset, the DVMP set, and ABC-6K and timed the generations for each method. On average, SD needs 4 seconds to generate an image, A&E 8.8 seconds, and SynGen 9.76 seconds.
+
+Hyperparameters. The hyperparameters we used consist of 50 diffusion steps, a guidance scale of 7.5, a scale-factor of 20, and 25 latent update steps. The choices of scale factor and latent update steps are described in Appendix B.2 and Appendix B.3 respectively.
+
+Parser. Throughout this project, we use the spacy parser with the out-of-the-box en_core_web_trf model.
+
+Attending word pieces. When a relatively uncommon word is encountered by the tokenizer of the text encoder, it is split to sub-words (i.e., word pieces). In the context of our loss function, when an entity (or modifier) is split into word pieces, we compute our distance function (the Symmetric-KL) for each word piece. Then, only the word piece that maximizes the distance is added to the loss.
+
+Cross-attention maps. We describe more formally the cross-attention maps on which we intervene. Let $N$ be the number of tokens in the prompt, and let $D ^ { 2 }$ be the dimensionality of the latent feature map in an intermediate denoising step. The denoising network defines a cross-attention map $A ^ { p a t c h e s  t o k e n s } \in \mathbb { R } ^ { D ^ { 2 } \times N }$ between each of $D ^ { 2 }$ patches in the latent feature map and each token. Intuitively, the attention maps designates which tokens are relevant for generating each patch.
+
+Atokens→patchesi c Our goal it to derive an attention distribution Atokens→patches ∈ RN×D2 ontains the attention distribution of token $i$ over patches. For this goal, we de- such that its $i$ -th row fine a score matrix $S$ to be the transpose of $A ^ { p a t c h e s  t o k e n s }$ , i.e,. a matrix whose $i ^ { t h }$ row contains the attention scores from each patch to token $i$ . Since $S$ is not normalized, we divide each row by its sum to get a distribution over patches. Unless stated otherwise, across the paper, we refer to $A ^ { t o k e n s  p a t c h e s } \ \in \ R ^ { N \times D ^ { 2 } }$ when mentioning the “cross-attention maps” $A$ and its $i ^ { t h }$ row $A _ { i }$ corresponding to the attention map from the $i ^ { t \tilde { h } }$ token.
+
+# B Additional Ablation Experiments
+
+# B.1 Further Investigation of the Positive and Negative Loss Terms
+
+In Section 4.3, we investigate the importance of the positive and negative loss function terms using a human rater. Here, we accompany the rating with a qualitative analysis, to examine the effect of each term. To this end, we generate images for 15 randomly selected prompts, five from each dataset. Fig. 8 depicts a sample of the generated prompts.
+
+We find that proper binding necessitates both the positive and negative terms: excluding the negative term from the loss function results in two noteworthy observations. First, the number of missing objects increase, evident by the missing crown, cat, metal chair, and tomato, in columns 1, 2, 4, and 5 in Fig. 8. One consequence of missing objects is the apparent improper binding, indicated by the red backpack and black shirt in columns 1 and 3.
+
+On the other hand, excluding the positive term results in fuzzier separation between objects. For instance, the cat is not completely formed, and is “merged” with the pillow; and while it appears that there is some green residue on the dog, it is not colored green. Moreover, the grass is green, which indicates a semantic leakage.
+
+![](images/9e9e5dc06f9ea57ae1f1a0533f48d135deab3224a48029e9cc8e0b580d738859.jpg)  
+Figure 8: We examine the effect of employing only one of the two losses instead of both. All images were generated using the same random seed.
+
+Putting these insights together, we observe that to some extent, the effect the loss terms is complementary. In addition to the increase of objects and proper binding, the images are more coherent (less cases of objects mixed into each other, such as the cat in the only-negative loss or the elephant in the only-positive loss).
+
+# B.2 Number of Timesteps for Intervention
+
+Recall that our method intervenes in latent denoising generation. In this appendix, we study the effect of the hyperparameters determining the number of steps in which we intervene.
+
+To identify an ideal number of timesteps to intervene, we experiment with 100 randomly selected prompts from the DVMP dataset, a fixed random seed, and a number of update steps from 5 to 50, in increments of 5. Examples of this experiment are shown in Fig. 9.
+
+We observe that when intervening in a small number of timesteps, our method failed to adequately mitigate semantic leakage or that images are not completely formed. For instance, the apple in column 1 in the 15-steps example is cartoon-ish, while the dog is not. Conversely, intervening for the full 50 timesteps resulted in an increase rate of blurred images (potentially due to the significant modification of the latent, which shifts it away from the learned distribution). We conclude that the optimal number of timesteps for intervention is 25, as this allows for effective mitigation of improper binding, while still generating visually appealing images.
+
+# B.3 Setting the Scale Factor
+
+The scale factor affects the update step size. Recall the update step stated in Section 2 $z ^ { \prime } t \ =$ $z _ { t } - \alpha \cdot \nabla z _ { t } \mathcal { L }$ . Here, $\alpha$ is the scale-factor.
+
+To determine a good selection for the scale-factor, we generate 100 randomly sampled prompts from the DVMP dataset, with a scale-factor value from 1 to 40, in increments of 10.
+
+As can be seen in Fig. 10, we observe that merely updating the latent using a scale-factor of 1 yields relatively good results in terms of improper binding, which confirms the utility of our loss function. However, such a low scale-factor also consistently leads to missing objects.
+
+![](images/14c8b17c6f6117e11f311dcd832a34148b3f96080a6cbc8bfeebe12e1b59e43c.jpg)  
+Figure 9: We experiment with varying number of diffusion steps and examine the effect of changing the number of diffusion steps for which we intervene with the cross attention maps. All images were generated using the same random seed.
+
+Interestingly, for greater scale-factor values, the generations become alike in their overall look, but are nonetheless very different. As an example, for both values, 10 and 30, the sliced banana is missing from the image in column 2, but the 30-value does result in a spotted teal skateboard. In column 3, values below 20 lead to images that contain two pandas (none of which are spotted), which indicates the proper binding process, and that the latent was not updated enough. On the other hand, a value greater than 20 leads to an image of a striped rabbit, instead of a spotted rabbit.
+
+One interesting conclusion from this experiment is that the greater the scale-factor, the stronger the concept separation. However, this is only true to a point. For a great enough value, generations become too blurred or simply lose their visual appeal.
+
+# C Additional Quantitative Analyses
+
+To study the efficacy of SynGen relative to the baselines in improper binding setting, we analyze the results under three perspectives. (1) as a function of repeating entities and modifiers; (2) as a function of the number of modifiers; and (3) degree of entanglement. Samples of generations are shown in Fig. 14.
+
+Number of repeating modifiers and entities. In this analysis, we examine the performance of all methods for prompts containing recurring modifiers (e.g., “a sliced strawberry and a sliced tomato) or entities (e.g., “a sliced tomato and a skewered tomato”). Aggregated results are illustrated in Fig. 11. Our observations reveal a decrease in performance across all methods when modifiers are repeated. However, the relative success between SynGen and the baselines in performance remains the same. Moreover, there is no substantial decline in results when entities are repeated.
+
+Number of modifiers in prompt. We hypothesize that since our method is specifically designed to tackle improper binding, it handles prompts containing many modifiers with more success. This is confirmed in Fig. 12, which shows the gap between SynGen and the baselines widens as the number of modifiers in a prompt increases.
+
+![](images/d3e6126585ec9bd960ed1564e6be9650118179689495909b8a146af48c2039d1.jpg)  
+Figure 10: Qualitative comparison between scale factor values for SynGen. For every prompt, the same seeds are applied. We anecdotally show our scale-factor value (we use the value 20) provides superior results.
+
+Entangled entities. As we describe in Section 4.2, entangled entities are strongly associated with their most common attribute. For instance, a tomato is typically red, and thus, it is common for images to depict red tomatoes.
+
+We categorize the prompts into three groups: (1) entangled prompts, which contain entangled entities with a modifier that overrides a common modifier (e.g., a purple strawberry); (2) common entangled prompts, which contain entangled entities with their common modifiers; and (3) neutral prompts, which do not contain entangled entities at all. Performance as a function of these groups is demonstrated in Fig. 13.
+
+# D Additional Qualitative Results
+
+# D.1 Qualitative analysis by number of modifiers
+
+In Fig. 15, examples from the DVMP challenge set include 2 to 6 modifiers.
+
+While errors of all types are prevalent regardless of the number of modifiers, their frequency tends to rise as more modifiers are added.
+
+As for SynGen, although it does not display semantic leakages at an increased rate compared to the baselines (as quantitatively demonstrated in Fig. 12), it does show a tendency to generate more than the specified number of entities as the modifier count increases. This behavior is observable in rows 8 and 10 for SynGen, and in rows 7 through 10 for the baselines.
+
+![](images/85f5607403abdc6870a56a4ce1c56b28f3be99bd268063b7a601bf66b072c663.jpg)  
+Figure 11: The performance of SynGen and the baselines in concept separation on prompts containing (a) repeating modifiers; and (b) repeating entities in the DVMP dataset.
+
+![](images/9d1cfc81fa2693efaaa104b4eccaf9320aa0ba71967dd7abb362cfb5c4d610ab.jpg)  
+Figure 12: Concept Separation as a function of number of modifiers in a prompt in the DVMP dataset, introduced in Section 3.2. Only the top-competing method (Attend-and-Excite) is plotted for readability.
+
+# D.2 Comparison to Spatial-Temporal Diffusion
+
+As described in Section 5, concurrent to this work, [24] developed a method to optimize the latents. While they primarily attend spatial and temporal relations, they too report on improper binding, namely, attribute mismatch. Thus, we extend the tables from Section 4, to include Spatial-Temporal Diffusion, see Fig. 16, Fig. 17, Fig. 18.
+
+Based on these 18 images, we observe that Spatial-Temporal Diffusion consistently misses at least one entity from the prompt. As an example, see Fig. 16. The images in columns 1 and 2 miss a crown (but include “wooden” objects), and columns 3 and 4 miss a lion and exhibit semantic leakage.
+
+In other cases, we note many cases of semantic leakage in and out of the prompt. For instance, in Fig. 18, in column 2 the clock is brown and the wall is pink, and in column 3, the chair is pink.
+
+![](images/8d3ccefc06ff7448bd5ce1ee70ad2999450d8b68cf62d374a9406a30462ae759.jpg)  
+Figure 13: The performance of SynGen and the baselines in concept separation when grouping the prompts with respect to entangled modifiers in the DVMP dataset.
+
+![](images/4ea6995a0851ecbdd9ea49de6414b5540a99ec6f3c458bb46205ab99a9827904.jpg)  
+Figure 14: Samples from the analyses in Appendix C. (a) a case of recurring entity (strawberry); (b) a recurring modifier (black) and entity (apple); (c) and (d) contain entangled entities (a blue bear and a purple strawberry); (e), (f), (g) are examples of prompts with more than two modifiers.
+
+![](images/5a2f2986eec6fbd64d3ae0e02ed85d26f35de8d75f51af7e28fc3e266a1ddda3.jpg)  
+Figure 16: Extended qualitative comparison for prompts from the DMVP dataset. SynGen and Spatial-Temporal Diffusion [24].
+
+![](images/953b95b2085f0eb27c3092007b6847efe94cb90428a63bc0c2f5dea26427b801.jpg)  
+Figure 15: Extended qualitative comparison for prompts from the DVMP challenge set.
+
+# D.3 Stable Diffusion and Structured Diffusion Comparison
+
+A comparison between Stable Diffusion and Structured Diffusion is depicted in Fig. 19. The findings from the study by [11] suggest that the generated images from Structured Diffusion are often similar to those generated by Stable Diffusion, with limited improvements in addressing semantic flaws and enhancing image quality. This is further supported by the comparable results presented in our findings Table 1. Therefore, while we include all baselines in our evaluations, our qualitative analysis only showcases images produced by the slightly superior Structured Diffusion.
+
+![](images/757bfb3c61e271ca9fc15534fb3114dcf5ff96c96a77179da1009f8c3ed96f12.jpg)
+
+![](images/fffaa9384b0aa8d332918a3c7d155fa067fc344945098a96ee49b8c6018a6cd1.jpg)  
+Figure 17: Extended qualitative comparison for prompts from the ABC6K dataset. SynGen and Spatial-Temporal Diffusion [24].   
+Figure 18: Extended qualitative comparison for prompts from the Attend-and-Excite dataset. SynGen and Spatial-Temporal Diffusion [24].
+
+![](images/c0d7a1455dedffcc865cde6b6fe1ff4740132809d18ece724df053fb66487420.jpg)  
+Figure 19: Side-by-side generations of StableDiffusion and StructureDiffusion.
+
+# E SynGen Failures
+
+We observe three recurring types of failure SynGen displays Fig. 20. First, when there are many modifiers and entities in the prompt, despite the results in Fig. 12, we note that sometimes the negative loss component becomes exceedingly large, and thus, pushes the latent out of the distribution the decoder was trained on. Consequently, images become blurred, or contain concepts which are successfully separated, but are incoherent. This is likely because our method over-fixates on incorporating all elements described in the prompt.
+
+Second, while SynGen typically successfully addresses the possible error cases described in Section 4.2, at times it can neglect generating all objects, unify separate entities, or neglect generating attributes. We conjecture that it is because the cross-attention maps of the modifier and its corresponding entity do not overlap enough. We note it usually occurs when there are many modifiers that refer to the same entity.
+
+Finally, as common with many diffusion models, we report a recurring issue with faithfulness to the number of units specified in the prompt, for a certain entity. For instance, upon receiving prompts containing “a strawberry”, SynGen generates images with multiple strawberries, instead of just one. One explanation to this problem is that the representation of a certain entity begins “scattered”, and is never quite formed into a single cluster. Interestingly, the opposite problem, where multiple units are “merged” into one, occurs far less in the generations of SynGen. Possibly, because of the inherent objective function of our loss, which “pushes away” foreign concepts from one another.
+
+![](images/ee8c2075e2aa32bc25142a215d072ab577fa45e2793cf9a8f2bbbda515b581bf.jpg)  
+Figure 20: Frequent failure modes in SynGen. (a) depicts a case of blurred image, (b) incoherent image which maintains concept separation. Both are a result of excessive updates to the latent, resulting from a large negative loss term. In example (c), the zebra and lion are merged into a single entity and (d) omits the sleepy lion. We conjecture (c) and (d) are a result of too little updates. (e) and (f) exhibit the well-known issue of flawed mapping between the number of units an entity is mentioned in the prompt to the generated image.
+
+# F The Diverse Multiple Modifiers Prompts (DVMP) dataset
+
+In Section 3.2 we describe DVMP, a new dataset containing rich and challenging combinations, for the purpose of evaluating improper binding.
+
+In total, DVMP has 18 types of objects, 16 types of animals, and 4 types of fruit. There are four animal modifiers, 7 object modifiers, two fruit modifiers, and 13 colors. A comprehensive account of the entities and their possible modifiers is shown in Table 4.
+
+# G Extended Evaluation
+
+# G.1 Additional Details on Human Evaluation Experiments
+
+In the manual evaluation procedure detailed in Section 3.3 the evaluator is tasked with comparing various image generations and selecting the optimal image based on multiple criteria. The guidelines and examples given to the evaluators are presented in Fig. 21 and Fig. 22. Fig. 23 provides a screenshot of the rating interface. The full results of the human evaluation are given in Table 5
+
+Rater Compensation. Raters were selected based on their performance history, requiring a minimum of 5,000 approved HITs with an approval rate exceeding $98 \%$ . They were required to pass a qualification exam with a perfect score before given access to the task. The hourly compensation was $\$ 10$ , ensuring fair renumeration for their contributions.
+
+Table 4: List of entities and their modifiers in the DVMP dataset. Colors are not restricted to categories.   
+
+<table><tr><td>Category</td><td>Entities</td><td>Modifiers</td></tr><tr><td>General</td><td>backpack, crown, suitcase, chair, balloon,bow, car, bowl,bench,clock, camera,umbrella, guitar, shoe, hat, surfboard, skateboard, bicycle</td><td>modern, spotted, wooden, metal, curved, spiky, checkered</td></tr><tr><td>Fruit</td><td>apple, tomato, banana, strawberry</td><td>sliced, skewered</td></tr><tr><td>Animals</td><td>cat, dog,bird,bear, lion,horse, elephant, monkey, frog, turtle,rabbit, mouse,panda, zebra, gorilla, penguin</td><td>furry, baby, spotted, sleepy</td></tr></table>
+
+<table><tr><td>Color Modifiers</td></tr><tr><td>red, orange, yellow, green, blue, purple, pink, brown, gray, black,white,beige, teal</td></tr></table>
+
+# Instructions
+
+·Please read the folowing_instructions carefully:   
+·Inthis task,youwillbe givenadescriptionand twoimages.Yourjobis toevaluatetheimages basedontwo criteria:   
+·1.Concept Separation: How well does the image match the given description?   
+·2.Visual Appeal: Which image looks overallbetter or more natural?   
+·ConceptSeparation:Foreachimage,askyourself: -Do you seeallobjects from thedescription? - Are all objects'details correct? - Are there any details on objects that should not be there? Choosethemagettatcstriptio.lfrealyodooeeallyoodandfeyealldo 'equally bad'.   
+·Visual Appeal: After evaluating Concept Separation,decide which image looks better or natural to you.   
+·Please choose theimages based on Concept Separation first,and then consider their Visual Appeal.
+
+Table 5: The population vote of three raters was normalized to sum to 100 and the standard error mean was added. The table reports the scores for concept separation (how well the image matches the prompt) and visual appeal for different models on each dataset.   
+
+<table><tr><td colspan="2">Dataset Model</td><td>Concept Separation</td><td>Visual Appeal</td></tr><tr><td rowspan="5"></td><td></td><td></td><td>40.11 ± 0.49</td></tr><tr><td>SynGen (ours) A&amp;E</td><td>38.80 ± 0.48 22.60 ± 0.41</td><td>21.47 ± 0.41</td></tr><tr><td>Structured Diffusion</td><td>09.98 ± 0.29</td><td>11.87 ± 0.32</td></tr><tr><td>Stable Diffusion</td><td>08.85 ±0.28</td><td>09.79 ± 0.29</td></tr><tr><td>No majority winner</td><td>19.77 ± 0.39</td><td>16.76 ± 0.37</td></tr><tr><td rowspan="5">DVMP (challenge set)</td><td>SynGen (ours)</td><td>29.22 ± 0.45</td><td>23.55 ± 0.42</td></tr><tr><td>A&amp;E</td><td>19.83 ± 0.39</td><td>19.00 ± 0.39</td></tr><tr><td>Structured Diffusion</td><td>09.00±0.28</td><td>15.56 ± 0.36</td></tr><tr><td>Stable Diffusion</td><td>09.89 ±0.29</td><td>15.56 ± 0.36</td></tr><tr><td>No majority winner</td><td>32.06 ± 0.46</td><td>26.33 ± 0.44</td></tr><tr><td rowspan="5">ABC-6K</td><td>SynGen (ours)</td><td>33.00 ± 0.47</td><td>25.72 ± 0.43</td></tr><tr><td>A&amp;E</td><td>17.84 ± 0.38</td><td>17.28 ± 0.37</td></tr><tr><td>Structured Diffusion</td><td>13.44 ± 0.34</td><td>14.50 ± 0.35</td></tr><tr><td>Stable Diffusion</td><td>11.72 ± 0.32</td><td>14.50 ± 0.35</td></tr><tr><td>No majority winner</td><td>24.00 ± 0.42</td><td>28.00 ± 0.44</td></tr></table>
+
+![](images/82d8574455ee4671180c38f1a36b8d085c7b413dbd94c64f2140afe00b0ee553.jpg)  
+Figure 22: Examples given to raters in their instructions. Each example consists of a prompt and two images: A good match (top) and a bad match (bottom) for the concept separation criterion. These examples were accompanied by text explaining why the images are considered a good (or bad) match to the prompt.
+
+![](images/b44574112cd54301447c0272d8f4bb1cbfb51941089509ca8b5d2789614429c0.jpg)  
+Figure 23: A screenshot of the AMT task. The order of images was randomized per HIT. “equally good” and “equally bad” were merged during post-processing into "no winner", to simplify presentation of results.
+
+# G.2 Phrases-to-Image Similarity
+
+A common approach to automatically assess text-based image generation is by computing the cosine similarity between an image and prompt, using a vision-language model like CLIP [9]. However, the very challenge we tackle here is rooted in CLIP’s failure in establishing correct mapping between syntactic bindings and visual bindings, functioning like a bag-of-words model [10]. As an example, suppose CLIP is prompted with “a blue room with a yellow window”. If we present CLIP with an image of a yellow room with a blue window, it may yield a similar score to an image that accurately depicts a blue room with a yellow window.
+
+In an attempt to address this flaw, we segment prompts to phrases containing entity-nouns and their corresponding modifiers (e.g., “a blue room” and “a yellow window”), and compute the similarity between these segmented phrases and the image. We then aggregate the result to a single score by computing the mean. With this approach, we expect CLIP to properly associate the modifiers (e.g., “blue” and “yellow”) with the correct entity-noun (i.e., “room” and “window”) as there is only one entity-noun in each segment. Unfortunately, this metric achieves relatively low agreement with the majority selection of human evaluation, only $4 3 . 5 \%$ of the time, where $25 \%$ is random selection. Despite the low agreement, we note the overall trend of selections of this automatic metric is very similar to the human majority selection. Table 6 shows the results of our automatic evaluation.
+
+Task
+
+"a white bicycle and a spiky bow"
+
+![](images/124756e90660410373b04cfda4dfb742cdd84e4515aefcc1bbbca2d14a872167.jpg)  
+Figure 24: A screenshot of the fine-grained AMT task.
+
+Table 6: Automatic evaluation of all methods on the three datasets. The table reports scores for concept separation (how well the image matches the prompt) and visual appeal. Values are the fraction of majority vote of three raters, normalized to sum to 100.   
+
+<table><tr><td>Method</td><td>DVMP (ours)</td><td>ABC-6K</td><td>A&amp;E</td></tr><tr><td>SynGen (ours)</td><td>47.33</td><td>41.33</td><td>44.63</td></tr><tr><td>A&amp;E</td><td>27.66</td><td>24.33</td><td>27.11</td></tr><tr><td>Structured Diffusion</td><td>12.84</td><td>17.84</td><td>11.87</td></tr><tr><td>Stable Diffusion</td><td>12.17</td><td>16.50</td><td>16.39</td></tr></table>

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+        "text": "Merging Models with Fisher-Weighted Averaging ",
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+        "text": "Michael Matena Colin Raffel Department of Computer Science University of North Carolina at Chapel Hill {mmatena,craffel}@cs.unc.edu ",
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+        "text": "Abstract ",
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+        "text": "Averaging the parameters of models that have the same architecture and initialization can provide a means of combining their respective capabilities. In this paper, we take the perspective that this “merging” operation can be seen as choosing parameters that approximately maximize the joint likelihood of the posteriors of the models’ parameters. Computing a simple average of the models’ parameters therefore corresponds to making an isotropic Gaussian approximation to their posteriors. We develop an alternative merging procedure based on the Laplace approximation where we approximate each model’s posterior as a Gaussian distribution whose precision matrix corresponds to its Fisher information. We first show that our “Fisher merging” technique provides a performance boost in settings where simple parameter averaging is currently used – specifically, robust fine-tuning and model ensembling. Then, we compare merging to standard gradient-based transfer learning and demonstrate that merging enables a fundamentally different method for transferring capabilities across models. Specifically, we show that Fisher merging is competitive with gradient-based transfer learning approaches (while being significantly cheaper) in intermediate-task training and domain-adaptive pre-training. We also show that our merging procedure makes it possible to combine models in previously unexplored ways. We release our code to facilitate future research into methods for merging models.1 ",
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+        "text": "1 Introduction ",
+        "text_level": 1,
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+        "text": "How should we transfer knowledge and capabilities across trained models? One popular approach is transfer learning [44], which fine-tunes a pre-trained model on a target task through additional gradient-based training. The preparatory step of pre-training the model on a data-rich task ideally instills useful “knowledge” into the network’s parameters, which allows the model to learn more rapidly and effectively when fine-tuned on a downstream task of interest. Transfer learning has therefore become a particularly important and omnipresent tool across many fields, including natural language processing [57, 13, 9, 52, 53, 46] and computer vision [43, 24, 68]. Recently, it has been shown that training on an “intermediate” task between pre-training and fine-tuning can further boost performance through additional transfer of capabilities from the intermediate task [47, 60, 51, 48]. Alternatively, continued self-supervised training on unlabeled domain-specialized data can serve as a form of domain adaptation [19]. ",
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+        "text": "All of the aforementioned transfer learning methods transfer knowledge by using a trained network to initialize another network followed by iterative gradient descent. While demonstrably powerful, several drawbacks arise from this: First, improvements to ancestor models cannot be passed down to descendants; instead, we must restart the whole process from the improved ancestor model, throwing away our previous work. For example, if we fine-tune a pre-trained model on a downstream task, but then the pre-trained model is improved through additional training, we must re-fine-tune the new model on our downstream task if we want to confer benefits from this additional pre-training. Furthermore, if we gain access to a checkpoint that has been fine-tuned on a useful intermediate task, we must again throw away our previous work and fine-tune from the intermediate task checkpoint. Existing methods for transfer learning also have the disadvantage of only being able to transfer information from a single model. While it may be possible to train on multiple intermediate tasks sequentially, one quickly either runs into a combinatorial explosion of saved checkpoints or faces the issue of “catastrophic forgetting” in continual learning [28]. In addition to slowing down experimentation by preventing reuse of work, these drawbacks impose limitations on the types of transfer that can occur. ",
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+            "Figure 1: Merging patterns considered in this work. Left: Merging many fine-tuned models as a form of ensembling. Center, top: “Robust fine-tuning” [66] , where a fine-tuned model is merged with the pre-trained model to improve performance on the original pre-training task. Center, bottom: Merging a fine-tuned model with a “donor” task, analogous to intermediate-task transfer learning [47, 51]. Right: Merging an intermediate-task trained model with a donor model. "
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+        "text": "A less common way of transferring capabilities across models is to simply average their parameters. This procedure, which we call “merging”, is generally only feasible when the models being averaged share a common architecture and initialization. Merging is the core component of the FedAvg algorithm used in Federated Learning [39], where updates to a shared model computed by individual workers that are training on different datasets are combined by simpling averaging the updates. Recently, Wortsman et al. [66] demonstrated that merging can be used to improve robustness to domain shift in fine-tuned models by averaging the parameters of the original pre-trained model with the fine-tuned parameters. Merging is also a common way of performing ensembling [49, 67], where the parameters of individual models trained on the same dataset are averaged to create a single performant model. ",
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+        "text": "In this work, we view model merging as approximately maximizing the joint likelihood of the models’ posterior distribution over parameters. Since gradient-based maximum likelihood training only provides a point estimate of the posterior, some approximation of the posterior distribution is required. When an isotropic Gaussian distribution is used to approximate the posterior (with identity precision matrix and mean set to the model’s parameter values), we show that maximizing the joint likelihood across models is equivalent to simply averaging their parameters. We therefore refer to merging models by averaging parameters as isotropic merging. The view of merging as maximizing the joint likelihood of model posteriors suggests that using a better estimate of the posterior distribution may yield improved merging results. This leads us to introduce Fisher merging, which leverages the Laplace approximation by using the diagonal of each model’s Fisher information as the precision matrix for that model’s posterior. ",
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+        "text": "Empirically, we demonstrate that merging models with Fisher merging outperforms isotropic merging in a variety of settings. We first focus on the existing applications of model ensembling [49, 67] and improving fine-tuned model robustness [66]. Then, we demonstrate for the first time that merging is a viable alternative to traditional gradient-based transfer learning. Specifically, we compare merging to intermediate-task transfer learning [47, 51] and domain-adaptive pre-training [19], finding that merging can achieve comparable performance at significantly lower cost. Additionally, we show that merging can provide an additional boost to models created via traditional intermediate-task training. This provides a concrete example of transfer that is fast and easy with merging but onerous or impossible to do with existing methods. Diagrams of the merging patterns we consider in this work are shown in fig. 1. ",
+        "bbox": [
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+        "text": "The rest of our paper is structured as follows: In section 2, we provide necessary background and detail our Fisher merging procedure. Section 3 provides experimental results on model ensembling, robust fine-tuning, intermediate-task training, and domain adaptation. We explore related works in section 4 and provide conclusions and thoughts on future work in section 5. ",
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+        "text": "2 Weighted Parameter Averaging for Model Merging ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our focus is on procedures for model merging, i.e. averaging the parameters of models that share an architecture and initialization. In this section, we first frame the common practice of averaging together model parameters as approximately maximizing the joint likelihood of model posteriors. Specifically, we show that parameter averaging corresponds to using an isotropic Gaussian as the approximate posterior for each model. We then introduce Fisher merging, which uses the model’s diagonal Fisher information matrix as the precision matrix of the Gaussian approximate posterior. Fisher merging can be implemented by setting each merged parameter value to a weighted average of the corresponding parameter values from the original models, with the weighting for each parameter determined by its Fisher information. In addition, we add model-level weightings as additional hyperparameters to set the relative importance of each model. ",
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+    {
+        "type": "text",
+        "text": "2.1 Isotropic merging ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Consider the problem setting where we have $M$ trained neural networks with parameters $\\theta _ { 1 } , \\dots , \\theta _ { M }$ and our goal is to create a single neural network with parameters $\\theta$ that, loosely speaking, inherits the capabilities of the $M$ trained neural networks. Assume that all of these neural networks share a common architecture and had the same set of initial parameter values before being trained. Merging attacks this problem by finding the parameters $\\theta$ that maximize the joint likelihood of the posterior distributions of the $M$ models. Unfortunately, typical neural network training procedures do not provide access to a posterior distribution, which necessitates approximation. If the posterior of each model is approximated via an isotropic Gaussian with mean set to the model’s parameters, the optimization problem can be written as $\\begin{array} { r } { \\theta ^ { * } = \\operatorname * { a r g m a x } _ { \\theta } \\sum _ { i } \\log p ( \\theta | \\theta _ { i } , I ) } \\end{array}$ where $p ( \\theta | \\theta _ { i } , I )$ is the probability distribution of the aforementioned approximate isotropic Gaussian posterior distribution used for model $i$ and $I$ is the identity matrix. This optimization problem has a closed-form solution given by $\\begin{array} { r } { \\theta ^ { * } = \\frac { 1 } { M } \\sum _ { i } \\theta _ { i } } \\end{array}$ , i.e. an average of the model parameters. Such an averaging procedure has been used in past work aiming to combine model capabilities, e.g. in federated learning [39], model ensembling [49, 67], and robust fine-tuning [66]. ",
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+    {
+        "type": "text",
+        "text": "2.2 Per-model weights ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this work, we additionally introduce model-specific scalar hyperparameters $\\lambda _ { i } , i \\in \\{ 1 , \\dots , M \\}$ into the model merging framework described above. Specifically, we change the optimization problem to $\\begin{array} { r } { \\theta ^ { * } = \\mathrm { a r g m a x } _ { \\theta } \\sum _ { i } \\bar { \\lambda } _ { i } \\log p ( \\underline { { \\theta } } | \\theta _ { i } , I ) } \\end{array}$ where $\\begin{array} { r } { \\lambda _ { i } \\geq 0 , \\bar { \\sum _ { i } } \\lambda _ { i } = \\bar { 1 } } \\end{array}$ . In the case of isotropic merging, this changes the solution to $\\theta ^ { * } = \\textstyle \\sum _ { i } \\lambda _ { i } \\theta _ { i }$ , These hyperparameters provide control over the importance assigned to each of the models that are being merged. For example, when using merging to perform ensembling we might expect each model to be equally important and therefore set $\\lambda _ { i } = 1 / M$ for all $i$ On the other hand, when mimicking the setup of intermediate-task training where the capabilities of a “donor” model are used to improve performance of a recipient model, we might weigh the recipient model more highly. Wortsman et al. [66] introduce a similar hyperparameter $\\alpha$ when averaging the parameters of two models and report results for varying values of $\\alpha$ . ",
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+    {
+        "type": "text",
+        "text": "2.3 Laplace Approximation ",
+        "text_level": 1,
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+        "text": "Framing merging as approximate maximization of the joint posterior likelihood reveals that simple parameter averaging is implicitly using an isotropic Gaussian posterior approximation. Such an approximation may be overly simplistic and lead to degraded performance. To explore improved merging procedures, we consider improved methods for creating an approximate posterior from a point estimate. Specifically, we use the Laplace approximation to the posterior, which corresponds to a second-order Taylor expansion of the log density around a mode [36, 10]. This leads to a Gaussian approximation $\\mathcal { N } ( \\theta , H ^ { - 1 } )$ of the posterior, where $H$ is the Hessian matrix and $\\theta$ are the model’s trained parameter values. More precisely, we assume that the parameter values $\\theta$ of a trained neural network are a local maximum of the posterior. It can then be shown that the precision matrix of the Laplace approximation is given by the Fisher information matrix of the network at $\\theta$ . ",
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+        "type": "text",
+        "text": "",
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+        "type": "text",
+        "text": "The Fisher information matrix $F _ { \\theta }$ [16, 3] of a neural network $p _ { \\theta } ( y | x )$ trained to predict an output $y$ from input data $x$ is a $\\left| \\theta \\right| \\times \\left| \\theta \\right|$ positive semidefinite matrix given by the formula ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/490a9cbdc83b948156f9c215372a5be8db425d9853519f29e24cb4ca4a2b9375.jpg",
+        "text": "$$\nF _ { \\theta } = \\mathbb { E } _ { x } \\left[ \\underset { y \\sim p _ { \\theta } ( y | x ) } { \\mathbb { E } } \\nabla _ { \\theta } \\log p _ { \\theta } ( y | x ) \\nabla _ { \\theta } \\log p _ { \\theta } ( y | x ) ^ { T } \\right] .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "It can be shown that the Fisher information matrix coincides with the Hessian $H$ at modes of the distribution [45], explaining its use in the Laplace approximation. The Fisher information matrix $F _ { \\theta }$ can also be used to relate changes in the model parameters to changes in the model output by noting that $\\begin{array} { r } { \\mathbb { E } _ { x } \\left[ D _ { \\mathrm { K L } } ( p _ { \\theta } ( y | x ) | | p _ { \\theta + \\delta } ( y | x ) ) \\right] \\approx \\frac { 1 } { 2 } \\delta ^ { T } F _ { \\theta } \\delta } \\end{array}$ as $\\delta  0$ , where $D _ { \\mathrm { K L } }$ denotes the KL-divergence [45]. ",
+        "bbox": [
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+        "type": "text",
+        "text": "As the full Fisher matrix takes $O ( | \\theta | ^ { 2 } )$ memory to store, it quickly becomes impractical for all but the smallest models. We are thus forced to use an approximation to the full Fisher in practice. In this paper, we follow the common practice of using the diagonal of the Fisher matrix [28]. While other methods (e.g. [1]) exist for estimating the Fisher, we leave their exploration for future work. In our experiments, we estimated the diagonal of the Fisher matrix via ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/2d1dd698e2cbe5fa0e307af3651d7ac0268cbc06468dc1e620074c171576b056.jpg",
+        "text": "$$\n\\hat { F } _ { \\theta } = \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } \\underset { y \\sim p _ { \\theta } ( y | x _ { i } ) } { \\mathbb { E } } ( \\nabla _ { \\theta } \\log p _ { \\theta } ( y | x _ { i } ) ) ^ { 2 } ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $x _ { 1 } , \\ldots , x _ { N }$ are drawn i.i.d. from the dataset that was used to train the model. The expectation over $y$ can be estimated via sampling from $p _ { \\theta } ( y | x _ { i } )$ or computed exactly when the number of classes is small. We note that computing the Fisher requires $N$ per-example gradients, which can be straightforwardly computed for neural networks using backpropagation. This makes computing the diagonal Fisher have roughly the same computational cost as training on $N$ examples. ",
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+    {
+        "type": "text",
+        "text": "2.4 Fisher Merging ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Having noted that the Laplace approximation provides a tractable way to obtain a better approximation to the posterior, we now use it to create an improved merging procedure that we call Fisher merging. Letting $F _ { 1 } , \\ldots , F _ { M }$ correspond to the diagonal approximate Fisher matrices, we construct $p ( \\boldsymbol { \\theta } | \\boldsymbol { \\theta } _ { i } , F _ { i } )$ as a Gaussian-distributed posterior over the parameters of the merged model with mean $\\theta _ { i }$ and precision $F _ { i }$ . To obtain the merged model, we find a single set of parameters that is given a high probability under all posteriors. Formally, we have ",
+        "bbox": [
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+    {
+        "type": "equation",
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+        "text": "$$\n\\theta ^ { * } = \\operatorname { a r g m a x } _ { \\theta } \\sum _ { i = 1 } ^ { M } \\lambda _ { i } \\log p ( \\theta | \\theta _ { i } , F _ { i } ) ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "which has the closed-form solution ",
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+    {
+        "type": "equation",
+        "img_path": "images/b9f9779e8422ae8554fad92087073b2a13cab2446907a429860af11f7a3ef5a9.jpg",
+        "text": "$$\n\\theta ^ { * ( j ) } = \\frac { \\sum _ { i = 1 } ^ { M } \\lambda _ { i } F _ { i } ^ { ( j ) } \\theta _ { i } ^ { ( j ) } } { \\sum _ { i = 1 } ^ { M } \\lambda _ { i } F _ { i } ^ { ( j ) } } ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $j = 1 , \\ldots , | \\theta |$ . Intuitively, we can think of Fisher merging as computing a weighted average of the parameter values in each model where the weighting is done according to each parameter’s Fisher information. Since the Fisher information is a local property of a single parameter value, Fisher merging might be less performant when applied to models whose parameters are far apart in parameter space. We therefore limit our focus to models that were trained from the same initialization. ",
+        "bbox": [
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+        "type": "text",
+        "text": "Numerical Issues. Note that (4) can run into numerical issues when the Fisher is close to zero across all models for a given parameter. In practice, we choose a privileged “target model” in all of our experiments and “default” to the parameter’s value in the target model in these cases. An alternative would be to take an average weighted only by the merging coefficients (i.e., pretend the Fisher is the same across all models). In practice, the choice of a “default” value for these parameters had little impact on performance (likely because a small Fisher value implies that changing the parameter has a minute effect on the model’s outputs and is therefore relatively unimportant to the model’s behavior). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Unmergeable Parameters. In many cases, we have some parameters from each model that do not appear in all of the models we are merging. For example, this includes having task-specific classification heads on top of a common body architecture. We handle this by only applying the merging procedure (3) to the shared body parameters and keeping the task-specific heads unchanged. Although this may lead to a distribution shift in the classification head inputs, we found it to work well in practice for the datasets and tasks we consider. ",
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+    {
+        "type": "text",
+        "text": "3 Experiments ",
+        "text_level": 1,
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+    },
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+        "type": "text",
+        "text": "Our first experimental goal is to validate that our use of an improved estimate of the posterior yields improved merging performance. To test this hypothesis, we apply Fisher merging to two settings where isotropic merging has already proven successful: Model ensembling [49, 67] and robust fine-tuning [66]. Then, we demonstrate that Fisher merging provides a cheap and effective alternative to traditional transfer learning pipelines by validating its performance in intermediate-task transfer learning [47, 51] and domain-adaptive pre-training [19]. Finally, we demonstrate that merging opens up new paths of transferring capabilities across models by demonstrating a boost in performance when merging an intermediate task-trained model with different donor models. ",
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+    {
+        "type": "text",
+        "text": "3.1 Ensembling ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "An existing application of isotropic merging is for ensembling, i.e. combining models trained on the same dataset to obtain better predictions. Ensembling is most commonly performed by averaging the predictions of the individual models. This form of ensembling requires computing the output of all $M$ models in the ensemble, thereby increasing the computational cost by a factor of $M$ compared to computing the output for a single model. A cheaper alternative is to average the parameters of the models themselves. This approach is diagrammed in fig. 1, left. Such an approach is used in the classical method of Polyak averaging [49], where parameter values from the final $M$ iterations of training are averaged. More recently, Wortsman et al. [67] introduced the “Model Soup” approach where fine-tuned models with different hyperparameter settings are averaged to improve performance. To the best of our knowledge, all parameter-averaging ensemble methods have used isotropic merging, i.e. an unweighted average. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To test whether Fisher merging provides a boost over isotropic merging when averaging parameters for ensembling, we consider ensembling fine-tuned checkpoints derived from the same pre-trained model. Specifically, we consider the BERT-Base model [13] fine-tuned on the RTE [8], MRPC [14], and SST-2 [59] datasets. For each dataset, we use five fine-tuned checkpoints downloaded from the Hugging Face model hub.2 These checkpoints were fine-tuned with a variety of hyperparameter settings that were not chosen by us, so our experimental setting most closely matches the “Model Soup” approach [67]. A list of the checkpoints used is available in appendix A. Since we do not anticipate that any member of the ensemble should be given a larger weight, we set $\\lambda _ { i } = 1 / 5$ for all models. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our results are shown in fig. 2. We report validation set scores for Fisher merging, isotropic merging, and prediction ensembling (specifically, averaging the output probabilties of all models). Fisher merging significantly outperforms isotropic merging in all cases and attains comparable performance to prediction ensembling. Notably, performing inference after merging is $M \\times$ cheaper than prediction ensembling, suggesting that merging can provide a cheaper alternative to standard ensembling procedures. ",
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+    {
+        "type": "text",
+        "text": "3.2 Robust Fine-Tuning ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Recently, Wortsman et al. [66] found that while fine-tuning a pre-trained vision model tends to improve performance on the downstream task, it also tends to decreases accuracy on the original pretraining task. They therefore propose a “robust fine-tuning” procedure called WiSE-FT that computes a weighted average of the original pre-trained parameters and the fine-tuned parameters. Different weighting values produce different trade-offs between pre-training and fine-tuning task performance. In some cases, robust fine-tuning can even improve performance on the original pre-training task without sacrificing performance on the downstream fine-tuning task relative to traditional fine-tuning. ",
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+    {
+        "type": "image",
+        "img_path": "images/fb688fa2108d6b2574b8ff9cd25a400ca0cd8488d56843978510fc021794970f.jpg",
+        "image_caption": [
+            "Figure 2: Validation set accuracy for ensembles of five fine-tuned BERT models using different ensembling methods on the RTE, MRPC, and SST-2 datasets. Fisher merging produces a single model that performs comparably to output ensembling while being $5 \\times$ cheaper. "
+        ],
+        "image_footnote": [],
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/475276917ba19ee94fd3aa6aad41698234d9d30623534e89916d5d9f5c0612ae.jpg",
+        "image_caption": [
+            "Figure 3: IID (ImageNet) and average outof-domain (OOD) accuracy across five OOD datasets when using the WiSE-FT procedure [66] with either Fisher or isotropic merging. Dark to light color indicates increasing $\\lambda _ { 1 }$ from 0 to 1. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "This procedure implicitly uses isotropic merging and therefore provides another natural testbed for determining whether Fisher merging provides a boost in performance. A schematic of robust fine-tuning is shown in fig. 1, center top. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We use the codebase and experimental setup of Wortsman et al. [66] exactly, simply replacing isotropic merging with Fisher merging. For full details of this setup, we refer to Wortsman et al. [66]. As a short summary, we apply WiSE-FT to the ImageNet [11, 58] pre-trained ViT-B/16 model [15] on five out-of-domain (OOD) datasets: ImageNet-A [21], ImageNet-R [20], ImageNet Sketch [62], ImageNet V2 [56], and ObjectNet [4]. Following Wortsman et al. [66], we measure IID (ImageNet) and OOD performance when averaging together the original pre-trained model parameters and parameters from models fine-tuned on each of the OOD datasets, varying $\\lambda _ { 1 }$ (the averaging weight for the pre-trained model, called $\\alpha$ by Wortsman et al. [66]) from 0 to 1 in 0.1-step increments (with $\\lambda _ { 2 } = 1 - \\lambda _ { 1 }$ correspondingly decreasing from 1 to 0). To determine whether Fisher merging confers a boost in performance, we compare parameter averaging using either isotropic or Fisher merging. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We plot the IID (ImageNet) accuracy against the average accuracy on the five OOD datasets for varying values of $\\lambda _ { 1 }$ in fig. 3, with plots for individual OOD datasets in fig. 7 (appendix). Fisher merging produces a significantly better trade-off between IID and OOD accuracy. In particular, Fisher merging seems to general improve IID accuracy compared to isotropic merging. For example, for the value of $\\lambda _ { 1 }$ producing the best average OOD accuracy, Fisher merging produces about $1 \\%$ higher IID accuracy than isotropic merging. ",
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+    {
+        "type": "text",
+        "text": "3.3 Intermediate-task training ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Having established that Fisher merging produces better results than isotropic merging in settings where merging has been attempted before, we now explore the use of merging as an alternative to a gradient-based transfer learning procedure. Specifically, we explore intermediate-task training [47, 51], where a model is fine-tuned on an intermediate “donor” task before being trained on the target task of interest. To the best of our knowledge, no prior work has considered parameter averaging as a way of performing intermediate-task transfer learning. For the most part, intermediate-task training has mainly been considered in the NLP domain; as such, we limit our experiments to the BERT [13] and RoBERTa [33] pre-trained language models. To enable comparison to past work, we mostly explored merging pairs of models but we are interested in exploring merging more than two models in future work. As in section 3.1, we made use of fine-tuned BERT and RoBERTa checkpoints from the Hugging Face repository [65]. ",
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+    {
+        "type": "text",
+        "text": "Following previous work [47, 51], we first ran experiments using BERT-base on the GLUE benchmark [61]. The GLUE benchmark consists of the sentence acceptability task CoLA [64], the sentiment detection task SST-2 [59], the paraphrase detection tasks MRPC and QQP [14, 23], the sentence similarity task STS-B [7], and the natural language inference (NLI) tasks MNLI, QNLI, RTE, and ",
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+        "img_path": "images/151508597749537ed623c9fc0f6b9eff5911b8e9f868ad563703b6f866df4f51.jpg",
+        "image_caption": [
+            "Figure 4: Validation set accuracy on RTE when performing intermediate-task training with datasets from GLUE as the donor task. Dashed line denotes RTE accuracy without intermediatetask training. "
+        ],
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+        "image_caption": [
+            "Figure 5: Validation accuracy on RTE after first fine-tuning on MNLI, then fine-tuning on RTE, and finally Fisher merging with various donor task models. Dashed line denotes RTE accuracy after MNLI intermediate-task training. "
+        ],
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+        "text": "WNLI [6, 54, 8, 31]. All of the GLUE tasks are classification tasks except for STS-B, which is a regression task with a score ranging from 0 to 5. To simplify computation of the Fisher, we turn STS-B into a classification task by partitioning the continuous label into 25 equally-sized buckets [53]. Following common practice, we do not run experiments on WNLI due to the tricks required to get a good score [12, 29]. See Wang et al. [61] for more details on these tasks and their associated metrics. We detail how we obtained fine-tuned checkpoints on these tasks in appendix C. We computed a diagonal Fisher approximation for each checkpoint using up to 4096 examples from the corresponding train set. Since it is not clear a priori what weighting coefficients $\\lambda _ { i }$ to use in this setting, we chose $\\lambda _ { i }$ by a grid search with 50 points, using the score on the first 2048 validation examples as the selection metric. We compare Fisher merging to isotropic merging as well as a standard gradient-based intermediate-task fine-tuning baseline [47]. A diagram of intermediate-task merging is shown in fig. 1, center bottom. ",
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+        "text": "In initial experiments (reported in tables A1 to A3), we performed intermediate-task training for possible pair of datasets from the GLUE benchmark. Congruent with past work [47, 51, 60], we found that intermediate-task training provided the most notable performance boost when the RTE dataset was the target. We therefore focus on RTE results in the main text. Figure 4 shows the results of intermediate-task training of BERT-base with RTE as the target task and the other GLUE datasets as donor tasks, using Fisher merging, isotropic merging, or standard gradient-based training. Notably, performing gradient-based intermediate-task training hurts on some datasets, whereas merging always helps. Fisher merging gets comparable or better performance than isotropic merging with the largest gap observed when using MNLI as the intermediate task. On the other hand, merging performs worse than standard gradient-based training when using MNLI as the donor task. ",
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+        "type": "text",
+        "text": "Exploring new paths for transfer Given this performance gap, we were interested to see whether merging could provide an additional boost on top of gradient-based intermediate-task training. We therefore performed Fisher merging on a BERT-base model that was first fine-tuned on MNLI and then fine-tuned on RTE. A diagram of this setup is shown in fig. 1, right. This procedure does not have a direct analog in traditional gradient-based, and as we will show later, performing multi-stage gradient-based intermediate-task training generally harms results. ",
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+        "text": "We consider Fisher merging the intermediate-task trained RTE model with all GLUE tasks and show the results in fig. 5. Fisher merging provides a boost over gradient-based intermediate-task training for all tasks. Interestingly, a boost is still conferred when merging with an MNLI-trained model, suggesting that merging provides a complementary path for transferring capabilities across models. ",
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+        "text": "Scaling to RoBERTa-large Seeing that merging can provide a boost on top of intermediate-task training, we explored whether this boost could still be obtained for a stronger model than BERTbase. We therefore applied the same procedure to a RoBERTa-large RTE model that had been fine-tuned from an MNLI intermediate checkpoint. Our donor models were the original RoBERTalarge checkpoint (i.e., not fine-tuned on MNLI) fine-tuned on MRPC, RTE, STS-B, and SST-2. We additionally ran a sequential gradient-based fine-tuning baseline where we started with the MNLI checkpoint, fine-tuned on the donor task, and then fine-tuned on the target task. ",
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+        "type": "text",
+        "text": "",
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+        "type": "text",
+        "text": "The results are shown in fig. 6. We find merging provides a boost in performance even on the more performant RoBERTa model. The largest boost of 2.2 points came from Fisher merging with another RTE checkpoint, which is reminiscent of using merging for ensembling. Notably, including an additional intermediate task in gradient-based training significantly harmed performance compared to performing intermediate-task training on MNLI alone. We hypothesize this is related to the phenomena of catastrophic forgetting [17], where the model’s capabilities on MNLI are forgotten as it is trained on the next intermediate task. Nevertheless, this illustrates model merging’s ability to sidestep the issue of catastrophic forgetting and enable exploration of novel transfer strategies. ",
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+        "text": "Costs We had previously noted that our merging procedure could potentially be substantially more efficient than standard gradient-based fine-tuning. To measure this claim concretely, we computed the FLOPs required for fine-tuning and merging an RTE checkpoint based on the heuristics described in Kaplan et al. [26]. Fine-tuning BERT-base on RTE for 10 epochs would require about 5.5e14 FLOPs. Our merging procedures require computing the merged checkpoint (eq. (4)) and then evaluating it on the validation set with Fisher merging also requiring the estimation of the Fisher matrix (eq. (2)) beforehand. These steps require about 4.0e8, 2.0e12, and 9.1e13 FLOPs respectively, resulting in a roughly $6 \\times$ lower total cost compared to fine-tuning for Fisher merging and $2 7 5 \\times$ lower cost for isotropic merging. We note that the Fisher matrix only needs to be computed once and can be reused for subsequent merges, which amortizes the most expensive step in Fisher merging. ",
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+        "type": "text",
+        "text": "To explore methods for further reducing costs, we experimented with using fewer examples to estimate the Fisher. Specifically, we experimented with intermediate-task Fisher merging of BERT-base with MNLI as the donor task and RTE as the target task. The results are shown in table A4. While using the full training set to estimate the Fisher produced the best performance $( 7 3 . 4 \\% )$ , using only 256 examples to estimate the Fisher only produced a mild degradation in accuracy $( 7 2 . 7 \\% )$ and still outperformed the isotropic merging baseline. This suggests that computing the Fisher over fewer examples could further reduce computational costs without sacrificing a great deal of accuracy. ",
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+        "text": "3.4 Domain Adaptation ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We now turn our attention to the “domain-adaptive pre-training” (DAPT) approach for domain adaptation advocated by Gururangan et al. [19], which is methodologically similar to intermediatetask training. DAPT consists of additional pre-training of an original general-purpose pre-trained checkpoint on domain-specific unlabeled data. We explore the benefits of merging in an experimental setup similar to Gururangan et al. [19]. We focus on the biomedical (BIOMED) and computer science (CS) domains because they correspond to the classification tasks that saw the largest gains from domain-adaptive pre-training in [19]. Namely, we experimented with the CHEMPROT [30] relation classification task on the BIOMED domain. On the CS domain, we used the citation intent task of ACL-ARC [25] and the relation classification task of SCIERC [35]. Following Gururangan et al. [19], we report macro- $F _ { 1 }$ for ACL-ARC and SCIERC, and we report micro- $F _ { 1 }$ for CHEMPROT. We used RoBERTa-base [33] as our baseline model. Appendix D includes full details of the pre-training, fine-tuning, and merging procedures used. ",
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+        "type": "text",
+        "text": "We present our results in table 1. Merging provided the largest boost on ACL-ARC, and outperformed traditional fine-tuning in this setting. We only observed a minor improvement in performance on CHEMPROT and SCIERC. We note that our boosts from gradient-based fine-tuning were smaller than reported in [19], which was likely because we were only able to train on public data and we applied domain-adaptive pre-training for fewer steps. However, our results are consistent in the sense that ACL-ARC received the largest boost and CHEMPROT received the smallest boost. ",
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+        "type": "text",
+        "text": "4 Related Work ",
+        "text_level": 1,
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+        "text": "Like our work, elastic weight consolidation (EWC) [28] uses the Laplace approximation to the posterior over model parameters to create a regularizer to prevent catastrophic forgetting in the context of continual learning. While their framework supports the use of posteriors from multiple ",
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+        "img_path": "images/e37e5ff6328092e1ce6fb3a999fcf9f5741c6f7644ef7f786581520308273af7.jpg",
+        "image_caption": [
+            "Figure 6: Validation accuracy on RTE using the setup of fig. 5, but with RoBERTa-large instead of BERT-base. “Standard training” fine-tunes on MNLI, then the donor task, then RTE. Dashed line denotes MNLI intermediate-task training. "
+        ],
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+    {
+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>ChemProt</td><td>ACL-ARC</td><td>SciERC</td></tr><tr><td>Unmerged</td><td>82.70.3</td><td>70.53.2</td><td>81.00.4</td></tr><tr><td>Fisher</td><td>83.10.4</td><td>73.21.7</td><td>81.30.5</td></tr><tr><td>Isotropic</td><td>82.80.4</td><td>72.52.3</td><td>81.70.5</td></tr><tr><td>Fine-tuned</td><td>82.50.1</td><td>71.53.0</td><td>81.61.0</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1: Domain adaptation results. “Unmerged” refers to checkpoints fine-tuned from RoBERTabase. “Fisher” and “Isotropic” refer to the result of merging those checkpoints with the domainadaptive pre-trained (DAPT) checkpoint. “Finetuned” refers to models fine-tuned from the DAPT checkpoint. Subscripts provide the standard deviation across five trials. ",
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+    {
+        "type": "text",
+        "text": "models as well, they restrict such models to be previous checkpoints of a continually trained model. EWC keeps the model from losing previously acquired knowledge while merging provides a means of directly adding new knowledge to a model. ",
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+        "type": "text",
+        "text": "Some other existing procedures such as distillation [22] and ensembling [42] can also be thought of as combining or transferring knowledge between neural networks. However, those methods represent knowledge solely through the output of models. The knowledge contained within the parameters of a network will necessarily be greater than the knowledge contained in its output [2]. Hence, methods that directly combine model parameters such as merging have the potential to be more powerful than those methods. Furthermore, our merging procedure has an efficient and closed-form solution (eq. (4)) while distillation requires iterative gradient descent-based training. ",
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+    {
+        "type": "text",
+        "text": "Isotropic checkpoint averaging is used by federated learning [39] and Polyak averaging [49]. However, the checkpoints merged by those methods can be thought of coming from the same training run of single model. We believe we are the first to demonstrate cross-task transfer coming from checkpoint averaging and to explore it in the context of transfer learning. However, adapting ideas from federated learning such as [32, 63] could provide a fruitful avenue for future model merging research. ",
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+    {
+        "type": "text",
+        "text": "Natural gradient descent refers to an optimization procedure that uses KL-divergence of model predictions as a distance measure rather than the Euclidean distance in parameter space employed by regular gradient descent [3]. It does this by performing gradient descent on a Riemannian manifold with the Fisher information matrix as its metric [45]. In practice, this amounts to using the Fisher as a preconditioner during gradient descent. Some work on natural gradient descent may prove relevant for model merging such as using Kronecker-factorized Fisher matrices as an alternative to the diagonal approximation employed in this paper [37, 18, 38]. More broadly, in the field of information geometry the Fisher information matrix plays the role of a metric on a Riemannian manifold [40]. This has led to explorations of model averaging using tools from information geometry, e.g. [5, 41, 50]. ",
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+        "type": "text",
+        "text": "5 Conclusion ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this paper, we introduced Fisher merging, a way to combine the capabilities of different models by computing a weighted average of their parameters. Fisher merging is motivated by a novel perspective of parameter averaging as maximizing the joint likelihood of model posteriors. Through extensive experiments, we demonstrated that using the Fisher information as a weight on the contribution of each parameter outperforms using an unweighted average. Furthermore, we showed that Fisher merging attains comparable and sometimes better performance than traditional gradient-based transfer learning methods at significantly lower costs. Our experiments also demonstrated various merging strategies that would be onerous with traditional gradient-based training, which opens up new avenues for transferring capabilities across models. In future work, we plan to investigate different methods for approximating the Fisher information and model posteriors as well as more esoteric combinations of models. ",
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+    {
+        "type": "text",
+        "text": "Acknowledgments and Disclosure of Funding ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "This work was supported by the NSF CAREER award under Grant No. 2145822. ",
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+    {
+        "type": "text",
+        "text": "References ",
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+        "type": "text",
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Systematic biology, 53(5), 2004.   \n[51] Pruksachatkun, Y., Phang, J., Liu, H., Htut, P. M., Zhang, X., Pang, R. Y., Vania, C., Kann, K., and Bowman, S. R. Intermediate-task transfer learning with pretrained models for natural language understanding: When and why does it work? arXiv preprint arXiv:2005.00628, 2020.   \n[52] Radford, A., Narasimhan, K., Salimans, T., and Sutskever, I. Improving language understanding by generative pre-training, 2018.   \n[53] Raffel, C., Shazeer, N., Roberts, A., Lee, K., Narang, S., Matena, M., Zhou, Y., Li, W., and Liu, P. J. Exploring the limits of transfer learning with a unified text-to-text transformer. arXiv preprint arXiv:1910.10683, 2019.   \n[54] Rajpurkar, P., Zhang, J., Lopyrev, K., and Liang, P. Squad: $1 0 0 { , } 0 0 0 { + }$ questions for machine comprehension of text. arXiv preprint arXiv:1606.05250, 2016.   \n[55] Rajpurkar, P., Jia, R., and Liang, P. Know what you don’t know: Unanswerable questions for squad. arXiv preprint arXiv:1806.03822, 2018.   \n[56] Recht, B., Roelofs, R., Schmidt, L., and Shankar, V. Do ImageNet classifiers generalize to ImageNet? In International Conference on Machine Learning (ICML), 2019.   \n[57] Ruder, S., Peters, M. E., Swayamdipta, S., and Wolf, T. Transfer learning in natural language processing. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Tutorials, pp. 15–18, 2019.   \n[58] Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., Huang, Z., Karpathy, A., Khosla, A., Bernstein, M., et al. ImageNet large scale visual recognition challenge. International journal of computer vision, 2015.   \n[59] Socher, R., Perelygin, A., Wu, J., Chuang, J., Manning, C. D., Ng, A. Y., and Potts, C. Recursive deep models for semantic compositionality over a sentiment treebank. In Proceedings of the 2013 conference on empirical methods in natural language processing, pp. 1631–1642, 2013.   \n[60] Vu, T., Wang, T., Munkhdalai, T., Sordoni, A., Trischler, A., Mattarella-Micke, A., Maji, S., and Iyyer, M. Exploring and predicting transferability across nlp tasks. arXiv preprint arXiv:2005.00770, 2020.   \n[61] Wang, A., Singh, A., Michael, J., Hill, F., Levy, O., and Bowman, S. R. Glue: A multitask benchmark and analysis platform for natural language understanding. arXiv preprint arXiv:1804.07461, 2018.   \n[62] Wang, H., Ge, S., Lipton, Z., and Xing, E. P. Learning robust global representations by penalizing local predictive power. In Advances in Neural Information Processing Systems (NeurIPS), 2019.   \n[63] Wang, H., Yurochkin, M., Sun, Y., Papailiopoulos, D., and Khazaeni, Y. Federated learning with matched averaging. arXiv preprint arXiv:2002.06440, 2020.   \n[64] Warstadt, A., Singh, A., and Bowman, S. R. Neural network acceptability judgments. Transactions of the Association for Computational Linguistics, 7:625–641, 2019.   \n[65] Wolf, T., Debut, L., Sanh, V., Chaumond, J., Delangue, C., Moi, A., Cistac, P., Rault, T., Louf, R., Funtowicz, M., et al. Huggingface’s transformers: State-of-the-art natural language processing. arXiv preprint arXiv:1910.03771, 2019.   \n[66] Wortsman, M., Ilharco, G., Li, M., Kim, J. W., Hajishirzi, H., Farhadi, A., Namkoong, H., and Schmidt, L. Robust fine-tuning of zero-shot models. arXiv preprint arXiv:2109.01903, 2021.   \n[67] Wortsman, M., Ilharco, G., Gadre, S. Y., Roelofs, R., Gontijo-Lopes, R., Morcos, A. S., Namkoong, H., Farhadi, A., Carmon, Y., Kornblith, S., and Schmidt, L. Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time. arXiv preprint arXiv:2203.05482, 2022.   \n[68] Yosinski, J., Clune, J., Bengio, Y., and Lipson, H. How transferable are features in deep neural networks? 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parse/dev/ek9a0qIafW/ek9a0qIafW.md

@@ -0,0 +1,454 @@
+# DIFFERENTIABLE PROMPT MAKES PRE-TRAINED LANGUAGE MODELS BETTER FEW-SHOT LEARNERS
+
+Ningyu Zhang1,2,3∗ Luoqiu $\mathbf { L i } ^ { 1 , 3 * }$ Xiang Chen1,3 Shumin Deng1,3 Zhen $\mathbf { B } \mathbf { i } ^ { 2 , 3 }$ Chuanqi Tan5 Fei Huang5 Huajun Chen1,3,4†
+
+1College of Computer Science and Technology, Zhejiang University   
+2School of Software Technology, Zhejiang University   
+3Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies   
+4Hangzhou Innovation Center, Zhejiang University   
+5Alibaba Group   
+{zhangningyu,3160102409,xiang chen,231sm,bizhen zju}@zju.edu.cn,   
+{chuanqi.tcq,f.huang}@alibaba-inc.com
+
+# ABSTRACT
+
+Large-scale pre-trained language models have contributed significantly to natural language processing by demonstrating remarkable abilities as few-shot learners. However, their effectiveness depends mainly on scaling the model parameters and prompt design, hindering their implementation in most real-world applications. This study proposes a novel pluggable, extensible, and efficient approach named DifferentiAble pRompT (DART), which can convert small language models into better few-shot learners. The main principle behind this approach involves reformulating potential natural language processing tasks into the task of a pre-trained language model and differentially optimizing the prompt template as well as the target label with backpropagation. Furthermore, the proposed approach can be: (i) Plugged to any pre-trained language models; (ii) Extended to widespread classification tasks. A comprehensive evaluation of standard NLP tasks demonstrates that the proposed approach achieves a better few-shot performance1.
+
+# 1 INTRODUCTION
+
+The pre-train—fine-tune paradigm has become the de facto standard for natural language processing (NLP), and has achieved excellent results in several benchmarks (Devlin et al., 2019; Liu et al., 2019; Lewis et al., 2020; Dong et al., 2019; Bao et al., 2020a). The success of these pioneers seems to suggest that large-scale pre-trained models are always nothing short of a panacea for boosting machine intelligence. However, supervised fine-tuning is still prone to labeled data in practice and faces unignorable challenges owing to the variations of domains, language, and tasks. These drawbacks lead to the research of an important technique, few-shot learning, which can significantly improve the learning capabilities of machine intelligence and practical adaptive applications by accessing only a small number of labeled examples.
+
+The GPT-3 model, introduced by Brown et al. (2020), exhibits impressive few-shot learning capabilities. Given a natural language prompt and 16 labeled samples as demonstrations in the contextual input, GPT-3 achieves $80 \%$ of the SOTA results. However, GPT-3 is a fully dense transformer model with 175B parameters, which makes it challenging to deploy in most real-world applications.
+
+Recently, an emerging fine-tuning methodology has arisen to equip smaller language models (LMs) with few-shot capabilities: adapting the pre-trained LM directly as a predictor through completion of a cloze task (Schick & Schutze (2021; 2020); Gao et al. (2020); Liu et al. (2021c)), which treats ¨ the downstream task as a (masked) language modeling problem. These prompts can be used in finetuning to provide the classifier with additional task information, especially in the low-data regime.
+
+![](images/2d898bc1ed7c35a8bba59819d5e1a3bda86d5be7afbd4b2b753bde9cf43a761c.jpg)  
+Figure 1: The architecture of DifferentiAble pRompT (DART) model comparing with MLM pretraining and conventional fine-tuning, where $T _ { i }$ and $Y _ { i }$ are unused or special tokens in the vocabulary. We leverage a few parameters within the language model as the template and label tokens and optimize them via backpropagation without introducing additional parameters apart from the model.
+
+Notably, Scao & Rush (2021) observe that prompting can often compensate for hundreds of data points on average across multiple classification tasks. However, determining the appropriate prompts requires domain expertise, and handcrafting a high-performing prompt often requires impractically large validation sets (Perez et al. (2021)). Recent studies (Lu et al. (2021); Zhao et al. (2021)) have reported that the manual prompt format can be sub-optimal, which would result in the accuracy varying from random guess performance to near the state-of-the-art. Therefore, previous approaches have attempted to search for discrete prompt tokens automatically. However, it is non-trivial for widespread classification tasks to obtain an optimized prompt template and target label token. For example, specific classification tasks such as relation extraction with the label of alternate name and country o f birth cannot specify a single label token in the vocabulary.
+
+In this paper, we propose a novel DifferentiAble pRompT (DART) fine-tuning approach, which is model-agnostic, parameter-efficient. As illustrated in Figure 1, the key idea is to leverage a few parameters (unused tokens) in the language model, which serve as the template and label tokens, and to optimize them in the continuous space using backpropagation. Subsequently, we introduce differentiable prompt learning to obtain optimized prompt templates as well as labels. Since fine-tuning with limited samples can be affected by instability (Dodge et al. (2020); Zhang et al. (2021)), we propose an optimization algorithm to jointly learning templates as well as labels. We further introduce an auxiliary fluency constraint object to ensure the association among the prompt embeddings.
+
+We conduct extensive experiments on $1 5 \mathrm { N L P }$ datasets. With only a few training samples across all the tasks, our approach (DART) can obtain a better performance. Notably, absolute performance improvement of up to $2 3 . 2 8 \%$ , over the conventional fine-tuning, is obtained on average in the setting of $K = 8$ (and $1 . 5 5 \%$ for fully supervised settings) on relation extraction datasets with complex label semantics. Our approach can be applied to real-world classification tasks without the high cost of collecting and annotating a large amount of data. The main contributions of this study are as follows:
+
+• We propose a new simple framework for few-shot learning, which is pluggable, extensible, and efficient. To the best of our knowledge, optimizing label tokens in continuous space is also a new branch of research that has not been explored in language model prompting.
+
+• A systematic evaluation of $1 5 \mathrm { N L P }$ tasks shows that the simple-yet-effective method contributes towards improvements across all these tasks. Remarkably, given only 8 labeled samples per class, our proposed approach can achieve $90 \%$ performance of the SOTA results (full dataset).
+
+# 2 RELATED WORK
+
+Language Model Prompting. The language model prompting has emerged with the introduction of GPT-3 (Brown et al. (2020)), which demonstrates excellent few-shot performance (Liu et al. (2021b)). However, GPT-3 is not designed for fine-tuning; it mainly relies on the handcraft prompt (in-context learning (Liu et al. (2021a); Zhao et al. (2021); Ding et al. (2021); Min et al. (2021))). Thus, recent studies (Qin & Eisner (2021); Hambardzumyan et al. (2021); Chen et al. (2021)) conducted in this field have been focused on automatically searching the prompts. Schick & Schutze (2021; ¨ 2020) propose the PET, which reformulates the NLP tasks as cloze-style questions and performs gradient-based fine-tuning. Tam et al. (2021) improve the PET with a denser supervision object during fine-tuning. Shin et al. (2020) propose the AUTOPROMPT to create prompts for a diverse set of tasks based on a gradient-guided search. Han et al. (2021) propose an approach called PTR, which leverages logic rules to construct prompts with sub-prompts for many-class text classification. Wang et al. (2021) reformulate potential NLP task into an entailment one, and then fine-tune the model with few-shot samples. Hu et al. (2021) propose an approach to incorporate external knowledge graph into the verbalizer with calibration. Additionally, Gao et al. (2020) present LM-BFF—better few-shot fine-tuning of language models, which leverages T5 (Raffel et al. (2020)) to generate templates and search label tokens in the vocabulary. However, the utilization of the generative model and the label search with validation is computation-intensive. Moreover, the prompt search over discrete space is sub-optimal due to the continuous nature of neural networks.
+
+To overcome these limitations, Liu et al. (2021c) propose P-tuning, which employs trainable continuous prompt embeddings learned by an LSTM. Zhong et al. (2021) propose an effective continuous method called OPTIPROMPT to optimize prompts for factual probing. Liu et al. (2021c) propose prefix-tuning, which keeps language model parameters frozen but optimizes a small continuous taskspecific vector for natural language generation tasks. Lester et al. (2021) propose a mechanism for learning “soft prompts” to condition frozen language models to perform downstream tasks. However, these approaches still have to optimize the external parameters (e.g., LSTM in P-tuning) and are prone to complex label space.
+
+Conversely, this study aims to develop a novel few-shot learning framework based on pre-trained language models which can reduce the prompt engineering (including templates and labels) and external parameter optimization. Furthermore, the proposed approach only leverages the noninvasive modification of the model, which can be plugged into any pre-trained language model and extended to the widespread classification task.
+
+Few-shot Learning. Few-shot learning can significantly improve the learning capabilities for machine intelligence and practical adaptive applications by accessing only a small number of labeled examples (Zhang et al. (2020)). The proposed approach corresponds to the other few-shot NLP methods, including: (1) Meta-learning (Yu et al. (2018); Bao et al. (2020b); Bansal et al. (2020); Deng et al. (2020b;a); Yu et al. (2020)), in which the quantities of the auxiliary tasks are optimized. (2) Intermediate training (Phang et al. (2018); Yin et al. (2020)), which supplements the pre-trained LMs with further training on the data-rich supervised tasks. (3) Semi-supervised learning (Miyato et al. (2017); Xie et al. (2020)), which leverages unlabeled samples. The proposed approach focuses on a more realistic few-shot setting (the number of labeled instances per class can be any variable).
+
+# 3 BACKGROUND
+
+Let $X _ { \mathrm { i n } } = \{ x _ { 1 } , x _ { 2 } , . . . , x _ { L } \}$ be a sentence, where $x _ { i }$ is the $i ^ { t h }$ token in the input sentence and $L$ is the number of tokens. Specifically, $X _ { \mathrm { i n } }$ is converted to a fixed token sequence $\tilde { X } _ { \mathrm { i n } }$ and then mapped to a sequence of hidden vectors $\{ \mathbf { h } _ { k } \in \mathbb { R } ^ { d } \}$ . Given the input sequence, $\tilde { X } _ { \mathrm { i n } } = [ \mathbb { C } \mathrm { L S } ] X _ { \mathrm { i n } } [ \mathrm { S E P } ]$ , the conventional fine-tuning approaches leverage a generic head layer over [CLS] embeddings (e.g., an MLP layer) to predict an output class. For the prompt-based method, a task-specific pattern string (template $\mathcal { T }$ ) is designed to coax the model into producing a textual output corresponding to a given class (label token ${ \mathcal { M } } ( Y ) _ { , }$ )—we refer to these two things together as a prompt. Specifically, $X _ { \mathrm { p r o m p t } }$ containing one [MASK] token is directly tasked with the MLM input as:
+
+$$
+X _ { \mathrm { p r o m p t } } = [ \mathrm { C L S } ] X _ { \mathrm { i n } } \ [ \mathrm { S E P } ] \mathcal { T } \ [ \mathrm { S E P } ]
+$$
+
+When the prompt is fed into the MLM, the model can obtain the probability distribution $p \big ( \mathrm { [ M A S K ] } \big | ( X _ { \mathrm { p r o m p t } } )$ of the candidate class, $y \in Y$ as:
+
+$$
+p ( y | X _ { \mathrm { p r o m p t } } ) = \sum _ { w \in \mathcal { V } _ { y } } p ( \mathrm { \ p A S K } ] = w | X _ { \mathrm { p r o m p t } } )
+$$
+
+where $w$ represents the $w ^ { t h }$ label token of class $y$
+
+# 4 OUR APPROACH
+
+# 4.1 MOTIVATION
+
+It can be observed from the previous empirical findings (Gao et al. (2020); Scao & Rush (2021)) that an optimal prompt is necessary for the improvement of the pre-trained language models for the few-shot learners. Since templates with discrete tokens may be sub-optimal and are insufficient to represent a specific class2, this study proposes DifferentiAble pRompT, referred to as DART, which can reduce the requirement of prompt engineering in order to improve the applicability of the proposed method in various domains.
+
+# 4.2 DIFFERENTIABLE TEMPLATE OPTIMIZATION
+
+Since the language tokens are discrete variables, finding the optimal prompts with token searching is non-trivial and may easily fall into the local minima. To overcome these limitations, we utilize pseudo tokens to construct templates and then optimize them with backpropagation. Specifically, given the template, $\mathcal { T } = \{ [ \mathrm { T } _ { 0 : i } ]$ ,[MASK], $\big [ \mathrm { T } _ { i + 1 : j } \big ] \big \}$ , which varies from the traditional discrete prompts, satisfying $[ \mathrm { T } _ { i } ] \in \mathcal { V }$ and map $\mathcal { T }$ into:
+
+$$
+\left\{ \mathbf { w } ( [ \mathrm { T } _ { 0 : i } ] ) , \mathbf { w } ( \mathrm { [ M A S K ] } ) , \mathbf { w } ( [ \mathrm { T } _ { i + 1 : m } ] ) \right\}
+$$
+
+DART considers $[ \mathrm { T } _ { i } ]$ as pseudo tokens and maps the template as follows:
+
+$$
+\{ h _ { 0 } , . . . , h _ { i } , \mathbf { w } ( \mathrm { ~ [ M A S K ~ ] ~ } ) , h _ { i + 1 } , . . . , h _ { m } \}
+$$
+
+where $h _ { i } ( 0 \leq i \leq j )$ are trainable parameters. Differentiable template optimization can obtain expressive templates beyond the original vocabulary $\mathcal { V }$ . Lastly, the templates, $h _ { i }$ , are differentially optimized by:
+
+$$
+\hat { h } _ { 0 : m } = \underset { h } { \arg \operatorname* { m i n } } \mathcal { L } \left( X _ { \mathrm { p r o m p t } } , y \right)
+$$
+
+Note that the values of the prompt embeddings, $h _ { i }$ , must be co-dependent with each other rather than independent. Unlike $\mathrm { \bf P }$ -tuning (Liu et al. (2021c)), which utilizes a bidirectional LSTM, DART leverages an auxiliary fluency constraint objective to associate the prompt embeddings with each other, thus stimulating the model to focus on context representation learning.
+
+# 4.3 DIFFERENTIABLE LABEL OPTIMIZATION
+
+Prompt-based fine-tuning requires filling in one word, and the masked word prediction is mapped to a verbalizer, which produces a class (i.e., ”Yes”: True. ”No”: False). For each class $c \in Y$ , the previous approaches such as LM-BFF (Gao et al. (2020)) estimate the conditional likelihood of the initial $\mathcal { L }$ on a pruned set $\mathcal { V } ^ { c } \subset \mathcal { V }$ of the top $k$ vocabulary words.
+
+However, the brute-forcing label searching: (1) is computationally intensive and tedious because the $\mathcal { D } _ { \mathrm { d e v } }$ is generally very large, requiring multiple rounds of evaluation. (2) has poor scalability with an increase in the class numbers (many classification datasets have more than 100 classes), the number of searches may be $k ^ { C }$ ( $C$ represents the total number of classes), which is exponential and thus intractable. Additionally, the labels of classes contain rich, complex semantic knowledge, and one discrete token may be insufficient to represent this information.
+
+Specifically, with the labels, $Y = \{ Y _ { 1 } , Y _ { 2 } , . . , Y _ { m } \}$ , different from the previous approach which converts the class type $Y _ { i }$ into a variable number of label tokens $\{ . . . , \nu _ { 1 } , . . . , \nu _ { k } , . . . \}$ , DART maps the $Y _ { j }$ to a continuous vocabulary space as follows:
+
+$$
+\begin{array} { r } { \mathcal { M } ( Y _ { j } ) = \{ h _ { m + j } \} , } \end{array}
+$$
+
+where $m$ is the number of trainable embedding in template. To avoid optimizing any external parameters, $\{ h _ { 1 } , . . . , h _ { m } , . . , h _ { m + n } \}$ is replaced with unused tokens (e.g., [unused1] or special tokens in vocabulary) in $\mathcal { V }$ to generate $\mathcal { V } ^ { \prime }$ , as shown in Figure 1.
+
+# 4.4 TRAINING OBJECTIVES
+
+Since the pseudo tokens in the prompt template must be co-dependent with each other, we introduce an auxiliary fluency constraint training without optimizing any other parameters inspired by Liu et al. (2021c); Tam et al. (2021). Overall, there are two objectives: the class discrimination objective $\mathcal { L } _ { C }$ and the fluency constraint objective $\mathcal { L } _ { F }$ .
+
+Class Discrimination Object The class discrimination objective is the main objective that aims to classify the sentences. As shown in Figure 1, given $( X _ { \mathrm { i n } } , \mathcal { T } )$ , we can generate $X _ { \mathrm { p r o m p t } }$ as:
+
+$$
+\mathcal { L } _ { C } = \mathrm { C E } \big ( g ( y | X _ { \mathrm { p r o m p t } } ) \big ) .
+$$
+
+where CE is the cross-entropy loss function, $\mathcal { L } _ { C }$ represents the class discrimination loss.
+
+Fluency Constraint Object To ensure the association among the template tokens and to maintain the ability of language understanding inherited from the PLMs, we leverage a fluency constraint object with the MLM. As shown in Figure 1, one token in the input sentence is randomly masked, and the masked language prediction is conducted. $x$ and $x ^ { \prime }$ are the original and masked sequences, respectively. Let $x ^ { m }$ be the target token that has been masked out in $x ^ { \prime }$ , and $g ( x ^ { m } | x ^ { \prime } , y )$ is maximized as follows3:
+
+$$
+h ( x ^ { m } | x ^ { \prime } , y ) = \frac { \exp ( \mathbb { [ } f ( x ^ { \prime } , y ) \mathbb { ] } | _ { x ^ { m } } ) } { \sum _ { \nu ^ { \prime } \in \mathcal { V } ^ { \prime } } \exp ( \mathbb { [ } f ( x ^ { \prime } , y ) \mathbb { ] } | _ { \nu ^ { \prime } } ) }
+$$
+
+$$
+\mathcal { L } _ { F } = \sum _ { m \in M } \mathrm { B C E } \big ( h ( x ^ { m } | x ^ { \prime } , y ) \big ) .
+$$
+
+By optimizing $\mathcal { L } _ { F }$ , the language model can obtain a better contextual representation with a rich association among the template tokens. We have the following training object:
+
+$$
+\boldsymbol { \mathcal { L } } = \boldsymbol { \mathcal { L } } \boldsymbol { c } + \boldsymbol { \lambda } \boldsymbol { \mathcal { L } } _ { F } ,
+$$
+
+where $\lambda$ is the hyper-parameter. Lastly, we introduce the overall optimization procedure of DART. To mitigate the instability of the few-shot fine-tuning, we jointly optimize templates and labels. Note that our approach can reuse the same transformer architecture (rather than additional LSTM) so that it enjoys the beauty of simplicity for prompt-tuning.
+
+Table 1: Our main results with RoBERTa-large. †: the full training set is used. $\ddagger$ : no training examples are used. Otherwise, we use $K = 1 6$ (# examples per class). We report mean (and standard deviation) performance over 5 different splits. Majority: majority class “GPT- $3 ^ { \circ }$ in-context learning: using the in-context learning proposed in with RoBERTa-large (no parameter updates); LM-BFF: we report the performance in Gao et al. (2020). full: fine-tuning using full training set.   
+
+<table><tr><td>Model</td><td>SST-2 (acc)</td><td>MR (acc)</td><td>CR (acc)</td><td>Subj (acc)</td><td>TREC (acc)</td></tr><tr><td>Majority†</td><td>50.9</td><td>50.0</td><td>50.0</td><td>50.0</td><td>18.8</td></tr><tr><td>Prompt-based zero-shot*</td><td>83.6</td><td>80.8</td><td>79.5</td><td>51.4</td><td>32.0</td></tr><tr><td>“GPT-3”in-context learning</td><td>84.8 (1.3)</td><td>80.5 (1.7)</td><td>87.4 (0.8)</td><td>53.6 (1.0)</td><td>26.2 (2.4)</td></tr><tr><td>Fine-tuning</td><td>81.4 (3.8)</td><td>76.9 (5.9)</td><td>75.8 (3.2)</td><td>90.8 (1.8)</td><td>88.8 (2.1)</td></tr><tr><td>LM-BFF</td><td>92.3 (1.0)</td><td>85.5 (2.8)</td><td>89.0 (1.4)</td><td>91.2 (1.1)</td><td>88.2 (2.0)</td></tr><tr><td>P-Tuning</td><td>92.2 (0.4)</td><td>86.7 (1.2)</td><td>91.8 (1.1)</td><td>90.3 (2.2)</td><td>86.3 (4.5)</td></tr><tr><td>DART</td><td>93.5 (0.5)</td><td>88.2 (1.0)</td><td>91.8 (0.5)</td><td>90.7 (1.4)</td><td>87.1(3.8)</td></tr><tr><td>Fine-tuning (full)+</td><td>95.0</td><td>90.8</td><td>89.4</td><td>97.0</td><td>97.4</td></tr><tr><td>Model</td><td>MNLI (acc)</td><td>SNLI(acc)</td><td>QNLI (acc)</td><td>MRPC (F1)</td><td>QQP (F1)</td></tr><tr><td>Majorityt</td><td>32.7</td><td>33.8</td><td>49.5</td><td>81.2</td><td>0.0</td></tr><tr><td>Prompt-based zero-shot*</td><td>50.8</td><td>49.5</td><td>50.8</td><td>61.9</td><td>49.7</td></tr><tr><td>“GPT-3” in-context learning</td><td>52.0 (0.7)</td><td>47.1 (0.6)</td><td>53.8 (0.4)</td><td>45.7 (6.0)</td><td>36.1 (5.2)</td></tr><tr><td>Fine-tuning</td><td>45.8 (6.4)</td><td>48.4 (4.8)</td><td>60.2 (6.5)</td><td>76.6 (2.5)</td><td>60.7 (4.3)</td></tr><tr><td>LM-BFF</td><td>68.3 (2.5)</td><td>77.1 (2.1)</td><td>68.3 (7.4)</td><td>76.2 (2.3)</td><td>67.0 (3.0)</td></tr><tr><td>P-Tuning</td><td>61.5 (2.1)</td><td>72.3 (3.0)</td><td>64.3 (2.8)</td><td>74.5 (7.6)</td><td>65.6 (3.0)</td></tr><tr><td>DART</td><td>67.5 (2.6)</td><td>75.8 (1.6)</td><td>66.7 (3.7)</td><td>78.3 (4.5)</td><td>67.8 (3.2)</td></tr><tr><td>Fine-tuning (full)+</td><td>89.8</td><td>92.6</td><td>93.3</td><td>91.4</td><td>81.7</td></tr></table>
+
+# 5 EXPERIMENTS
+
+In this section, we detail the comprehensive experimental results conducted on classification tasks. The promising results demonstrate that our proposed DART substantially outperforms the conventional fine-tuning method, thus, making pre-trained language models better few-shot learners.
+
+# 5.1 DATASET STATISTICS
+
+We conduct a comprehensive study across $1 5 \mathrm { N L P }$ tasks, which covers sentiment analysis, natural language inference, paraphrases, sentence similarity, relation extraction, and event extraction (We only report event argument extraction performance). The evaluation consisted of 10 popular sentence classification datasets (SST-2, MR, CR, Subj, TREC, MNLI, SNLI, QNLI, MRPC, QQP).To further evaluate the effectiveness of the proposed approach with complex label space, we conduct experiments on the relation extraction and event extraction datasets, including SemEval-2010 Task 8 (Hendrickx et al., 2010), TACRED-Revisit (Alt et al. (2020)), Wiki $8 0 ^ { 4 }$ (Han et al., 2019), ChemProt (Kringelum et al., 2016), and $\mathrm { A C E } { - } 2 0 0 5 ^ { 5 }$ .
+
+# 5.2 SETTINGS
+
+The proposed model is implemented using Pytorch (Paszke et al. (2019)). Our experiments are conducted with the same setting following LM-BFF ( Gao et al. (2020)), which measures the average performance with a fixed set of seeds, $S _ { \mathrm { s e e d } }$ , across five different sampled $\mathcal { D } _ { \mathrm { t r a i n } }$ for each task. We utilize a grid search over multiple hyperparameters and select the best result as measured on $\mathcal { D } _ { \mathrm { d e v } }$ for each set $\left\{ \mathcal { D } _ { \operatorname { t r a i n } } ^ { s } , \mathcal { D } _ { \operatorname { d e v } } \right\} , s \in \mathcal { S } _ { \mathrm { s e e d } }$ . We employ AdamW as the optimizer. We conduct experiments with a RoBERTa-large (Liu et al. (2019)) on classification tasks for a fair comparison with LM-BFF. We leverage an uncased BERT-large (Devlin et al. (2019)) for relation extraction datasets, except that we use SCIBERT (Beltagy et al. (2019)) for the ChemProt dataset. We follow Soares et al. (2019) and use special entity markers uniformly to highlight the entity mentions for relation extraction.
+
+Table 2: Results on RE dataset WiKi80 (accuracy), while other datasets (micro $\mathrm { F } _ { 1 }$ ). We use $K = 8 , 1 6 , 3 2$ (# examples per class). Full represents the full training set is used.   
+
+<table><tr><td rowspan=1 colspan=1>Dataset</td><td rowspan=1 colspan=1>Model</td><td rowspan=1 colspan=1>K=8</td><td rowspan=1 colspan=1>K=16</td><td rowspan=1 colspan=1>K=32</td><td rowspan=1 colspan=1>Full</td></tr><tr><td rowspan=1 colspan=1>SemEval</td><td rowspan=1 colspan=1>Fine-tuningLM-BFFDART</td><td rowspan=1 colspan=1>26.343.251.8 (+25.5)</td><td rowspan=1 colspan=1>43.862.067.2 (+23.4)</td><td rowspan=1 colspan=1>64.272.977.3 (+13.1)</td><td rowspan=1 colspan=1>87.888.089.1 (+1.3)</td></tr><tr><td rowspan=1 colspan=1>TACRED-Revisit</td><td rowspan=1 colspan=1>Fine-tuningLM-BFFDART</td><td rowspan=1 colspan=1>7.421.025.8 (+18.4)</td><td rowspan=1 colspan=1>15.523.730.1 (+14.6)</td><td rowspan=1 colspan=1>25.827.131.8 (+6.0)</td><td rowspan=1 colspan=1>75.076.477.8 (+2.8)</td></tr><tr><td rowspan=1 colspan=1>WiKi80</td><td rowspan=1 colspan=1>Fine-tuningLM-BFFDART</td><td rowspan=1 colspan=1>46.366.568.5 (+22.2)</td><td rowspan=1 colspan=1>60.373.575.2 (+14.9)</td><td rowspan=1 colspan=1>70.078.179.4 (+9.4)</td><td rowspan=1 colspan=1>87.586.288.1 (+0.6)</td></tr><tr><td rowspan=1 colspan=1>ChemProt</td><td rowspan=1 colspan=1>Fine-tuningLM-BFFDART</td><td rowspan=1 colspan=1>30.255.057.2 (+27.0)</td><td rowspan=1 colspan=1>41.556.160.8 (+19.3)</td><td rowspan=1 colspan=1>52.560.063.1 (+10.6)</td><td rowspan=1 colspan=1>79.579.181.0 (+1.5)</td></tr></table>
+
+Table 3: Ablation of DART with different components on SemEval. ( $\mathrm { F T = }$ Fine tuning)   
+
+<table><tr><td>Method</td><td>K=8</td><td>K=16</td><td>K=32</td><td>Full</td></tr><tr><td>Conventional FT</td><td>26.3</td><td>43.8</td><td>64.2</td><td>87.8</td></tr><tr><td>DART</td><td>51.8</td><td>67.2</td><td>77.3</td><td>89.1</td></tr><tr><td>-fluency constraint object</td><td>50.3 (-1.5)</td><td>66.1 (-1.1)</td><td>76.0 (-1.3)</td><td>88.2 (-0.9)</td></tr><tr><td>-differentiable template</td><td>49.8 (-2.0)</td><td>66.3 (-0.9)</td><td>76.2 (-1.1)</td><td>88.4 (-0.7)</td></tr><tr><td>-differentiable label</td><td>47.5 (-4.3)</td><td>62.5 (-4.7)</td><td>73.7 (-0.6)</td><td>87.8 (-1.3)</td></tr></table>
+
+# 5.3 MAIN RESULTS
+
+As shown in Table 1, we observe that our approach obtains better performance than conventional fine-tuning and achieves comparable results with LM-BFF. Note that DART can reduce the prompt engineering without external models (e.g., T5 in LM-BFF) to generate templates that are readily easy to adapt to other datasets. DART can obtain $1 1 . 3 \%$ improvement with only 16 training samples per class on the MR dataset, comparable with LM-BFF, which leverages T5 to generate appropriate prompts. These results indicate that DART can better stimulate potential ability and makes the pretrained language model a better few-shot learner. We also notice that DART yields better performance than P-tuning, which indicates that label optimization is beneficial.
+
+For the classification tasks with the complex label space, as shown in Table 2 and Figure 2(a), we observe that DART outperforms the conventional fine-tuning approach as well as LM-BFF with a large margin on relation extraction and event extraction datasets in both the few-shot and fully supervised settings. The proposed approach achieves an improvement of $2 . 8 \%$ of the absolute performance on the TACRED-Revisit dataset with full supervision and yields $1 8 . 4 \%$ gains with only 8 training samples per class. These findings also indicate that more relevant templates and labels can be determined without expert intervention, making it possible to generalize the proposed approach to other domains. We attribute the significant improvements to the fact that, unlike the GLUE datasets containing small categories, in relation extraction and event extraction tasks, the datasets consist of a large number of classes with complex label space, making it more challenging to obtain suitable label tokens. Furthermore, we notice that the improvement decays slowly when $K$ becomes larger (i.e., from 8 to 32). Our approach is a simple yet effective fine-tuning paradigm that can reduce prompt engineering within the complex label space, thus, making it possible to be an appropriate plug-in for some SOTA models.
+
+# 5.4 ABLATION STUDY
+
+We conduct an ablation study to validate the effectiveness of the components in the proposed approach. We observe that DART exhibits a performance decay in the absence of any one of the modules, i.e., fluency constraint object, differentiable template, or differentiable label, demonstrating that all the modules are advantageous. Furthermore, we notice that differentiable label optimization is more sensitive to performance and is highly beneficial for DART, especially for low-resource settings. Since the proposed approach is the first approach that utilizes the differentiable label optimization, these findings illustrate that a suitable label token is important.
+
+![](images/b053255abd2ecc3272a6f14f2f44fc8e5650e3e34a452a5a1695656a01cd072b.jpg)  
+Figure 2: (a) Few-shot results using the ACE-2005. We used $\mathrm { K } = 4$ , 8, 16, and 32 (# examples per class) with BERT. $\mathrm { F T = }$ Fine-tuning) (b) BERT-large vs. GPT-2-medium results for the SemEval. Moreover, for lower K, our method consistently outperforms conventional fine-tuning.
+
+# 5.5 ANALYSIS AND DISCUSSION
+
+CAN DART BE APPLIED TO OTHER PRE-TRAINED LMS?
+
+To evaluate whether the proposed approach can be applied to other LMs, we conduct experiments using GPT-2-medium6 . From Figure 2(b), we observe that DART with GPT-2-medium yields better performance than the conventional fine-tuning approach. Furthermore, we notice that DART with GPT-2-medium can achieve performance on par with BERT-large, as observed by Liu et al. (2021c), indicating that the potential of GPT-style architectures for natural language understanding has been underestimated.
+
+WHY DO DIFFERENTIABLE PROMPTS YIELD BETTER PERFORMANCE?
+
+To further analyze why our differentiable prompts method yields better performance compared with prompts with fixed templates and label tokens, we visualize the representation of masked tokens in the CR dataset during different training steps (from left to right) as shown in Figure 3 (fixed) and 4 (differentiable), respectively. While both methods learn separable hidden states, differentiable prompts’ representation is relatively more compact while the representation generated from fixed prompts is more scattered. This observation of differentiable prompts generating more discriminative representations than the fixed prompts method is supported by an indicator $R _ { D }$ , the ratio between average intra-class and average inter-class distance. We believe the main reason behind its better performance lies in the more discriminative representation of the differentiable method. More details can be found in Appendix A.6.
+
+WHAT EXACTLY IS OPTIMIZED PROMPT?
+
+Since prompt templates and label tokens in the proposed approach are mapped as $\{ h _ { 1 } , . . . , h _ { m } , . . , h _ { m + n } \}$ , we further analyze what exactly optimized label learned. We conduct a nearest-neighbor vocabulary embedding search to project the Top-3 optimized pseudo-label tokens in $\mathcal { V }$ to a readable natural language.We use $t$ -SNE (Van der Maaten & Hinton (2008)) with normalization to visualize labels on Wiki80 dataset. For example, “military branch” refers to as red $\star$ in Figure 5 represents the relation type, which is learned by optimizing the pseudo label in the continuous space, and the “volunteered”, “corporal” and “buddies”, refers to as • are the tokens closest to the label. This finding indicates that the differentiable method generates better semantic representation.
+
+![](images/b44a78b2125f9d44df025e26c4e4bd56dfbd5dfa119652316c81f62d989614cc.jpg)  
+Figure 3: Visualization of masked tokens’ representation in different training steps (with training 10, 30, 50, 70 steps from left to right) with fixed prompts.
+
+![](images/f3373a894e545a25d4cdd06493f5cd0ea1c7c220a06fa9b5563541f84f6f551e.jpg)  
+Figure 4: Visualization of masked tokens’ representation in different training steps (with training 10, 30, 50, 70 steps from left to right) with differentiable prompts.
+
+# DART V.S. CONVENTIONAL FINE-TUNING
+
+The ability of DART to perform few-shot learning can be attributed to the label and being a true language understanding task, that once the model is capable of performing it correctly, it can easily apply this knowledge to other tasks that are framed as such. Superficially, (i) DART does not optimize any new parameters; however, conventional fine-tuning should learn an explicit classifier head over [CLS] embeddings, which may fail in the low-data regime. (ii) DART has the same task setting as large-scale language model pre-training.
+
+# 6 CONCLUSION AND FUTURE WORK
+
+![](images/f9c23adbce1f98a1397de326791db9413d35e4f43e0ae5d3992dc1374af6d665.jpg)  
+Figure 5: A 3D visualization of several label representations learned in DART.
+
+This paper presents DART, a simple yet effective finetuning approach that improves the fast-shot learning pretrained language model. The proposed approach can produce satisfactory improvements in the few-shot scenarios when compared to the conventional finetuning approaches. The proposed method is also pluggable for other language models (e.g., BART) and can be extended to other tasks, such as intent detection and sentiment analysis. Intuitively, the results obtained in this study can be used to stimulate future research directions in the few-shot or lifelong learning for NLP.
+
+# ACKNOWLEDGMENTS
+
+We want to express gratitude to the anonymous reviewers for their hard work and kind comments. This work is funded by National Key R&D Program of China (Funding No.SQ2018YFC000004), NSFCU19B2027/NSFC91846204, Zhejiang Provincial Natural Science Foundation of China (No. LGG22F030011), Ningbo Natural Science Foundation (2021J190), and Yongjiang Talent Introduction Programme (2021A-156-G).
+
+# REPRODUCIBILITY STATEMENT
+
+Our code is available in https://github.com/zjunlp/DART for reproducibility. Hyperparameters are provided in the Appendix A.1.
+
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+
+# A APPENDIX
+
+Our code is available in the supplementary materials for reproducibility. This section contains details about the training procedures and hyperparameters for each of the datasets. We utilize Pytorch (Paszke et al., 2019) to conduct experiments with 1 Nvidia 3090 GPUs. All optimizations are performed with the AdamW optimizer with a linear warmup of learning rate over the first $10 \%$ of gradient updates to a maximum value, then linear decay over the remainder of the training. Gradients are clipped if their norm exceeds 1.0, and weight decay on all non-bias parameters is set to 0.01. Early stopping is adopted to reduce over-fitting on the training set.
+
+We follow LM-BFF (Gao et al., 2020) to measure the average performance of models trained on 5 different randomly sampled $\mathcal { D } _ { \mathrm { t r a i n } }$ and $\mathcal { D } _ { \mathrm { d e v } }$ splits, and perform grid search for optimal hyper-parameter combinations on each split, including learning-rate, weight decay, and batch size.
+
+For P-tuning (Liu et al., 2021c), due to the limit of search space, we do not set anchor tokens in prompt tokens.
+
+For DART, we adopt joint optimization to acquire optimal prompts and fine-tune over global parame ters. Note that we use base prompts as templates of pseudo tokens to accelerate convergence.
+
+To compare fairly, we use RoBERTa-large (Liu et al., 2019) as pre-trained model for both DART and P-tuning framework, following LM-BFF (Gao et al., 2020). We also adopt the best discrete prompts together with label words in LM-BFF as base prompt settings for each framework, as stated below.
+
+A.1 HYPER-PARAMETER SEARCH SPACE OF OUR METHOD IN GRID SEARCH
+
+SST-2, MR, CR, Subj, TREC, QNLI, MRPC, QQP
+
+The hyper-parameter search space is (the optimal set of parameters may vary across different tasks and data splits):
+
+• learning rate [1e-5, 5e-5, 1e-4, 2e-4] • weight decay [0.0, 0.01, 0.05, 0.10] • number epochs [20,30] • batch size: [4, 8, 16, 24, 32] • max seq length: 128 • gradient accumulation steps: [1, 2]
+
+MNLI, SNLI
+
+The hyper-parameter search space is (the optimal set of parameters may vary across different tasks and data splits):
+
+• learning rate [1e-5, 5e-5, 1e-4, 2e-4] • weight decay [0.0, 0.01, 0.05, 0.10] • number epochs [30,40]   
+• batch size: [4, 8, 16]   
+• max seq length: 256   
+• gradient accumulation steps: [1, 2]
+
+# TACRED-Revisit, WiKi80, SemEval
+
+The hyper-parameter search space are:
+
+• learning rate [3e-5,5e-5,1e-5,5e-6]   
+• number epochs [20,30]   
+• batch size: 48   
+• max seq length: 128   
+• gradient accumulation steps: 2
+
+# ChemProt
+
+The hyper-parameter search space are:
+
+• learning rate [3e-5,5e-5,1e-5,5e-6]   
+• number epochs [20,30]   
+• batch size: 48   
+• max seq length: 256   
+• gradient accumulation steps: 4
+
+# DialogRE
+
+The hyper-parameter search space is (the optimal set of parameters may vary across different tasks and data splits):
+
+• learning rate [1e-5, 5e-5, 1e-4, 2e-4]
+
+• weight decay [0.0, 0.10]   
+• number epochs [20,30,40]   
+• batch size: [4, 8]   
+• max seq length: 256   
+• gradient accumulation steps: [1, 2]
+
+A.2 BASE PROMPT AND LABEL WORDS
+
+# SST-2, MR, CR
+
+• prompt template $( l e n g t h = 3$ ) [”text”, ”it”, ”was”, ”<mask>”, ”.”] • label words $\{ \ ' 0 ^ { \ast }$ : ”terrible”, ”1”: ”great”}
+
+# Subj
+
+• prompt template ${ l e n g t h = 3 }$ ) [”text”, ”This”, ”is”, ”<mask>”, ”.”] • label words $\{ \ ' 0 ^ { \ast }$ : ”incorrect”, ”1”: ”correct”}
+
+# TREC
+
+• prompt template $( l e n g t h = 1 $ ) [”<mask>”, ”:”, ”text”]   
+• label words $\{ \ ' 0 ^ { \ast }$ : ”Description”, ”1”:”Entity”,”2: ”Expression”,”3”: ”Human”,”4”: ”Location”,”5”:”Number”}
+
+# MNLI, SNLI
+
+• prompt template(length $= 2$ ) [”texta”, ”?”, ”<mask>”, ”,”, ”textb”] • label words {”contradiction”: ”No”,”entailment”: ”Yes”, ”neutral”: ”Maybe”}
+
+QNLI
+
+• prompt template $( l e n g t h = 2 )$ ) [”texta”, ”?”, ”<mask>”, ”,”, ”textb”] • label words {”not entailment”: ”No”,”entailment”: ”Yes”}
+
+# MRPC, QQP
+
+• prompt template(length $= 2$ ) [”texta”, ”?”, ”<mask>”, ”,”, ”textb”] • label words $\{ { } ^ { \ ' } 0 ^ { \ ' } \colon { } ^ { \ ' } \mathrm { N o } ^ { \ ' }$ , ”1”: ”Yes”}
+
+# TACRED-Revisit, WiKi80, SemEval,DialogRE
+
+• prompt template $\mathit { l e n g t h } = 3$ ) [”text”, Entity1, ”is”, ”the”, ”<mask>”, ”of”, Entity2] • label words {”country of origin”, ”participating team”, ”participant of”,...}
+
+A.3 TEMPLATE LENGTH ANALYSIS
+
+<table><tr><td>Model</td><td>Accuracy</td></tr><tr><td>DART (length = 2)</td><td>92.6 (0.6)</td></tr><tr><td>DART(length = 3)</td><td>93.5 (0.5)</td></tr><tr><td>DART (length = 5)</td><td>91.2 (1.1)</td></tr><tr><td>DART (length = 10)</td><td>90.6 (0.5)</td></tr><tr><td>Fine-tuning</td><td>81.4 (3.8)</td></tr></table>
+
+Table 4: Few-shot performance on SST-2 task using templates with different length.
+
+We define the length of a template as the number of tokens except for input sentence and <mask> token, and apply DART on templates with different length. The performance of a specific template length $l$ is derived by summarizing the averaging accuracy on each few-shot data splits, using template $T = t _ { 1 } , t _ { 2 } , . . . , t _ { l }$ . From the Table 4, we observe that for the SST-2 task, the model whose template length is three yield best performance; however, the overall impact of template length is rather insignificant as models with different template length obtain relatively similar performance.
+
+A.4 PERFORMANCE ON FULL TRAINING SET   
+Table 5: Full training set results with RoBERTa-large. Fine-tuning: we reported same results as Gao et al. (2020). LM-BFF: we trained LM-BFF model (without demonstration) on full-training set.   
+
+<table><tr><td>Model</td><td> SST-2 (acc)</td><td>MR (acc)</td><td>CR (acc)</td><td>Subj (acc)</td><td>TREC (acc)</td></tr><tr><td>Fine-tuning</td><td>95.0</td><td>90.8</td><td>89.4</td><td>97.0</td><td>97.4</td></tr><tr><td>LM-BFF</td><td>94.9</td><td>91.9</td><td>92.4</td><td>96.9</td><td>97.3</td></tr><tr><td>DART</td><td>94.6</td><td>91.3</td><td>93.8</td><td>96.6</td><td>95.6</td></tr><tr><td>Model</td><td>MNLI (acc)</td><td> SNLI (acc)</td><td>QNLI (acc)</td><td>MRPC (F1)</td><td>QQP (F1)</td></tr><tr><td>Fine-tuning</td><td>89.8</td><td>92.6</td><td>93.3</td><td>91.4</td><td>81.7</td></tr><tr><td>LM-BFF</td><td>89.6</td><td>90.3</td><td>92.8</td><td>91.7</td><td>86.4</td></tr><tr><td>DART</td><td>87.3</td><td>89.5</td><td>92.3</td><td>90.4</td><td>89.5</td></tr></table>
+
+We conduct experiments and report the performance of DART with full-sized training data of GLUE tasks. From Table 5, we notice that DART obtain better or comparable results compared with the standard fine-tuning and LM-BFF, indicating that prompt-based tuning methods benefit less from full-sized data.
+
+# A.5 PERFORMANCE WITH CONSTRAINED LABEL TOKENS
+
+We conduct a nearest neighbor vocabulary embedding search to project the best optimized differentialble label token to a readable natural token. Those tokens are chosen based on cosine-similarity between all tokens’ embedding and the optimized differentialble label token of DART. We list them in descending order with similarity scores (i.e., the token ‘great‘ is chosen as its cosine-similarity score with trained positive label embedding of DART is the highest among all tokens, and the token ‘terrible‘ is the most similar token with the trained negative label embedding; the other tokens are selected and listed in descending order with similarity scores). From Table 6, we observe that the performance of fixed prompt models is related to the similarity score of the chosen label token and that the DART model learns more semantic representation for label tokens, thus, yield best performance.
+
+Table 6: Few-shot performance on CR task using constrained label tokens with DART.   
+
+<table><tr><td>Label tokens</td><td>Accuracy</td></tr><tr><td>differentiable token (DART)</td><td>91.8 (0.5)</td></tr><tr><td>great/terrible</td><td>91.5 (0.3)</td></tr><tr><td>fantastic/awful</td><td>91.0 (0.6)</td></tr><tr><td>amazing/horrible</td><td>90.2 (0.8)</td></tr><tr><td>good/bad</td><td>89.6 (0.5)</td></tr></table>
+
+![](images/0c61fc567d406c3af111e4cc5884a126add33c3e4fa142be3aa73b25148d217f.jpg)  
+Figure 6: The $R _ { D }$ ratio curve on dev set of CR task of fixed prompt and differentiable prompt during training.
+
+# A.6 MORE EXPERIMENTS
+
+We numeralize our observation on representation of masked token with a ratio between the average intra-class distance and average inter-class distance of hidden state vectors as $\begin{array} { r } { R _ { D } = \frac { \bar { D } _ { i n t r a } } { \bar { D } _ { i n t e r } } } \end{array}$ D¯ intra , where:
+
+$$
+\begin{array} { r } { \bar { D } _ { i n t r a } = \displaystyle { \frac { 1 } { C } \sum _ { c = 1 } ^ { C } \bar { D } _ { i n t r a ( c ) } = \frac { 1 } { C } \sum _ { c = 1 } ^ { C } \frac { 1 } { N _ { c } } \sum _ { i = 1 } ^ { N _ { c } } \sum _ { j = 1 } ^ { N _ { c } } \mathrm { d i s t a n c e } \left( H _ { c } [ i ] , H _ { c } [ j ] \right) } ; } \\ { \bar { D } _ { i n t e r } = \displaystyle { \frac { 1 } { C ( C - 1 ) } \sum _ { c _ { 1 } = 1 } ^ { C } \sum _ { c _ { 2 } \neq c _ { 1 } } \bar { D } _ { i n t e r ( c _ { 1 } , c _ { 2 } ) } = \frac { 1 } { C ( C - 1 ) } \sum _ { c _ { 1 } = 1 } ^ { C } \sum _ { c _ { 2 } \neq c _ { 1 } } \sum _ { i = 1 } ^ { N _ { c _ { 1 } } N _ { c _ { 2 } } } \mathrm { d i s t a n c e } \left( H _ { c _ { 1 } } [ i ] , H _ { c _ { 2 } } [ j ] \right) } ; } \end{array}
+$$
+
+where distance is the euclidean metric between two vectors, and $H _ { c } [ i ]$ means the hidden state representation of masked token of $i$ -th sample from class $c$ . For discriminative representation, its average intra-class distance is low as data points within the same class tend to gather together, and its average inter-class distance is high as data points from different classes are separated, so its $R _ { D }$ ratio should be close to 0.
+
+As is shown in Figure 6, the $R _ { D }$ ratio of the differentiable method grows lower than that of the fixed label method, which shows the hidden state representation trained in the differentiable method has better linear separability.
+
+Note that in a masked language model, a linear transformation is performed on the hidden state representations, with a linear decoder sharing weights with the model’s word embeddings serving as the final token classifier. Hence it is evident that better linear separability of the representations leads to better performance. In our case, the differentiable method yields better performance due to its better linear separability.
+
+# A.7 LIMITATIONS
+
+Our work may fail when the distribution of the task corpus varies from that of the pre-training corpus. For example, a general pre-trained language model may be fine-tuned with more training instances in a specific domain (e.g., medical domain). This issue can be addressed by intermediate training (Phang et al., 2018; Yin et al., 2020; Zhao et al., 2021), and will be analyzed in the future work. Besides, our work also shows an instability associated with hyper-parameters which is also observed by Dodge et al. (2020); Zhang et al. (2021); Perez et al. (2021) as volatility of few-shot learning in NLP. Overall, however, we believe our work will inspire future work to few-shot settings with more practical applications to low-data settings, e.g., that involve low-resource languages or expert annotation.
+
+# A.8 BROADER IMPACT
+
+The pre-train-fine-tune approach has become the standard for natural language processing (NLP). However, supervised fine-tuning is still practically affected by labeled data. This study proposes a novel pluggable, extensible, and efficient approach named DifferntiAble pRompT (DART), which can convert small language models into better few-shot learners. We believe that our study makes a significant contribution to the literature because determining the appropriate prompts requires domain expertise, and handcrafting a high-performing prompt often requires impractically large validation sets, and these issues have been overcome with the use of the proposed method, which is model-agnostic, parameter-efficient. We experimentally verified our proposed approach on 13 standard NLP tasks, and it was seen to outperform several standard NLP platforms.

parse/dev/nVV6S2sb_UL/nVV6S2sb_UL.md

@@ -0,0 +1,393 @@
+# Securing Secure Aggregation: Mitigating Multi-Round Privacy Leakage in Federated Learning
+
+# Abstract
+
+Secure aggregation is a critical component in federated learning (FL), which enables the server to learn the aggregate model of the users without observing their local models. Conventionally, secure aggregation algorithms focus only on ensuring the privacy of individual users in a single training round. We contend that such designs can lead to significant privacy leakages over multiple training rounds, due to partial user selection/participation at each round of FL. In fact, we show that the conventional random user selection strategies in FL may lead to leaking users’ individual models within a number of rounds that is linear in the number of users. To address this challenge, we introduce a secure aggregation framework, MultiRoundSecAgg, with multi-round privacy guarantees. In particular, we introduce a new metric to quantify the privacy guarantees of FL over multiple training rounds, and develop a structured user selection strategy that guarantees the long-term privacy of each user (over any number of training rounds). Our framework also carefully accounts for the fairness and the average number of participating users at each round. Our experiments on MNIST, CIFAR-10 and CIFAR-100 datasets in the IID and the non-IID settings demonstrate the performance improvement over the baselines, both in terms of privacy protection and test accuracy.
+
+# 18 1 Introduction
+
+19 Federated learning (FL) enables collaborative   
+20 training of machine learning models over the   
+21 data collected and stored locally by multiple   
+22 data-owners. The training in FL is typically   
+23 coordinated by a central server who maintains a   
+24 global model that is updated locally by the users.   
+25 The local updates are then aggregated by the   
+26 server to update the global model. Throughout   
+27 the training process, the users never share their   
+28 data with the server, i.e., the data is always kept   
+29 on device, rather, they only share their local   
+30 updates. However, as has been shown recently,   
+31 the local models may still reveal substantial   
+32 information about the local datasets, and the   
+33 private training data can be reconstructed from   
+34 the local models through inference or inversion   
+35 attacks (see e.g., [11, 26, 42, 12]).   
+36 To prevent such information leakage, secure aggregation protocols are proposed (e.g., [4, 31, 15,   
+37 40, 2, 38, 30]) to protect the privacy of the local models, both from the server and the other users,   
+38 while still allowing the server to learn their aggregate. More specifically, the secure aggregation   
+39 protocols ensure that, at any given round, the server can only learn the aggregate model of the users,   
+40 and beyond that no further information is revealed about the individual model.   
+41 Secure aggregation protocols, however, only ensure the privacy of the individual users in a single   
+42 training round, and do not consider their privacy over multiple training rounds [4, 2, 31, 32]. On   
+43 the other hand, due to partial user selection [7, 5, 6, 28], the server may be able to reconstruct the   
+44 individual models of some users using the aggregated models from the previous rounds. In fact, we   
+45 show that after a sufficient number of rounds, all local models can be recovered with a high accuracy   
+46 if the server uniformly chooses a random subset of the users to participate at every round. As shown   
+47 in Fig.1, performing model inversion attack [12] with the recovered local models yields reconstructed   
+48 images with a similar quality as the original images.
+
+![](images/2b7ac1d582e3b2a93e737316b90b25ddee4cbaf2e92b6e52c676e0124cd02db1.jpg)  
+Figure 1: A qualitative comparison of the reconstructed images in two settings is shown. The first setting corresponds to the case that model privacy with random user selection (e.g., FedAvg [25]) is protected by conventional secure aggregation schemes as [4] at each round. In the second setting, our proposed method ensures the long-term privacy of individual models over any number of rounds, and hence model inversion attack cannot work well. This reconstruction process is described in detail in Appendix H.
+
+Contributions. As such motivated, we study long-term user privacy in FL. Specifically, our 50 contributions are as follows.
+
+1. We introduce a new metric to capture long-term privacy guarantees for secure aggregation protocols in FL for the first time. This long-term privacy requires that the server cannot reconstruct any individual model using the aggregated models from any number of training rounds. Using this metric, we show that the conventional random selection schemes can result in leaking the local models after a sufficient number of rounds, even if secure aggregation is employed at each round.
+
+2. We propose Multi-RoundSecAgg, a privacy-preserving structured user selection strategy that ensures the long-term privacy of the individual users over any number of training rounds. This strategy also takes into account the fairness of the selection process and the average number of participating users at each round.
+
+3. We demonstrate that Multi-RoundSecAgg creates a trade-off between the long-term privacy guarantee and the average number of participating users. In particular, as the average number of participating users increases, the long-term privacy guarantee becomes weaker.
+
+4. We provide the convergence analysis of Multi-RoundSecAgg, which shows that the long-term privacy guarantee and the average number of participating users control the convergence rate. The convergence rate is maximized when the average number of participating users is maximized. (e.g., the random user selection strategy maximizes the average number of participating users at the expense of not providing long-term privacy guarantees). As we require stronger long-term privacy guarantees, the average number of participating users decreases and a larger number of training rounds is required to achieve the same level of accuracy as the random selection strategy.
+
+5. Finally, our experiments in both IID and non-IID settings on MNIST, CIFAR-10 and CIFAR-100 datasets demonstrate that Multi-RoundSecAgg achieves almost the same test accuracy compared to the random selection scheme while providing better long-term privacy guarantees.
+
+# 73 2 Related Work
+
+74 The underlying principle of the secure aggregation protocol in [4] is that each pair of users exchange a   
+75 pairwise secret key which they can use to mask their local models before sharing them with the server.   
+76 The pairwise masks cancel out when the server aggregates the masked models, allowing the server to   
+77 aggregate the local models. These masks also ensure that the local models are kept private, i.e., no   
+78 further information is revealed beyond the aggregate of the local models. This protocol, however,   
+79 incurs a significant communication cost due to exchanging and reconstructing the pairwise keys.   
+80 Recently, several works have developed computation and communication-efficient protocols [31, 15,   
+81 2, 35, 8, 10, 38], which are complementary to and can be combined with our work. Another line of   
+82 work focused on designing partial user selection strategies to overcome the communication bottleneck   
+83 in FL while speeding up the convergence by selecting the users based on their local loss [7, 5, 6, 28].   
+84 Previous works, either on secure aggregation or on partial user selection, however, do not consider   
+85 mitigating the potential privacy leakage as a result of partial user participation and the server observing   
+86 the aggregated models across multiple training rounds. While [27] pointed out to the privacy leakage   
+87 of secure aggregation, mitigating this leakage has not been considered and our work is the first secure   
+88 aggregation protocol to address this challenge.
+
+Differential privacy (DP), in which each user adds artificial noises to the local models, can be one of the potential solution to protect the privacy leakage over the multiple rounds [9, 1, 37, 3, 16]. In DP, however, the privacy guarantee sacrifices the model performance, which is known as a privacy-utility trade-off. It is worth noting that secure aggregation and DP are complementary, i.e., all the benefits of DP can be applied to our approach by adding noise to the local models [3]. In this paper, our objective is to understand the secure aggregation itself.
+
+# 95 3 System Model
+
+96 In this section, we first describe the basic federated learning model in Section 3.1. Next, we introduce   
+97 the multi-round secure aggregation problem for federated learning and define the key metrics to   
+98 evaluate the performance of a multi-round secure aggregation protocol in Section 3.2.   
+100 We consider a cross-device federated learning setup consisting of a server and $N$ users. User $i \in [ N ]$   
+101 has a local dataset $\mathcal { D } _ { i }$ consisting of $m _ { i } = | \mathcal { D } _ { i } |$ data samples. The users are connected to each other   
+102 through the server, i.e., all communications between the users goes through the server [24, 4, 17].   
+103 The goal is to collaboratively learn a global model $_ x$ with dimension $d$ , using the local datasets that   
+104 are generated, stored, and processed locally by the users. The training task can be represented by   
+105 minimizing a global loss function,
+
+$$
+\operatorname* { m i n } _ { x } L ( x ) { \mathrm { ~ s . t . ~ } } L ( x ) = { \frac { 1 } { \sum _ { i = 1 } ^ { N } w _ { i } } } \sum _ { i = 1 } ^ { N } w _ { i } L _ { i } ( x ) ,
+$$
+
+106 where $L _ { i }$ is the loss function of user $i$ and $w _ { i } \geq 0$ is a weight parameter assigned to user $i$ to specify   
+107 the relative impact of that user. A common choice for the weight parameters is $w _ { i } = m _ { i }$ [17]. We   
+108 define the optimal model parameters $x ^ { * }$ and $\boldsymbol { x } _ { i } ^ { * }$ as $x ^ { * } = \arg \operatorname* { m i n } _ { x \in \mathbb { R } ^ { d } } L ( x )$ and $\begin{array} { r } { \boldsymbol { x } _ { i } ^ { * } = \arg \operatorname* { m i n } _ { \boldsymbol { x } \in \mathbb { R } ^ { d } } L _ { i } ( \boldsymbol { x } ) } \end{array}$ .   
+109 Federated Averaging with Partial User Participation. To solve (1), the most common algorithm   
+110 is the FedAvg (federated averaging) algorithm [24]. FedAvg is an iterative algorithm, where the model   
+111 training is done by repeatedly iterating over individual local updates. At the beginning of training   
+112 round $t$ , the server sends the current state of the global model, denoted by $x ^ { ( t ) }$ , to the users. Each   
+113 round consists of two phases, local training and aggregation. In the local training phase, user $i \in [ N ]$   
+114 updates the global model by carrying out $E \left( \geq 1 \right)$ local stochastic gradient descent (SGD) steps and   
+115 sends the updated local model $x _ { i } ^ { ( t ) }$ to the server. One of key features of cross-device FL is partial   
+116 device participation. Due to various reasons such as unreliable wireless connectivity, or battery issues,   
+117 at any given round, only a fraction of the users are available to participate in the protocol. We refer   
+118 to such users as available users throughout the paper. In the aggregation phase, the server selects   
+119 $K \leq N$ users among the available users if this is possible and aggregates their local updates. The   
+120 server updates the global model as follows
+
+$$
+\pmb { x } ^ { ( t + 1 ) } = \sum _ { i \in S ^ { ( t ) } } w _ { i } ^ { \prime } \pmb { x } _ { i } ^ { ( t ) } = \mathbf { X } ^ { ( t ) ^ { \top } } \pmb { p } ^ { ( t ) } ,
+$$
+
+where 121 ${ \mathbf { } } S ^ { ( t ) }$ is the set of participating users at round $t$ , $\begin{array} { r } { w _ { i } ^ { \prime } = \frac { w _ { i } } { \sum _ { i \in S ^ { ( t ) } } w _ { i } } } \end{array}$ , and ${ \pmb p } ^ { ( t ) } \in \{ 0 , 1 \} ^ { N }$ is the   
+122 corresponding characteristic vector. That is, $\pmb { p } ^ { ( t ) }$ denotes a participation vector at round $t$ whose $i$ -th   
+123 entry is 0 when user $i$ is not selected and 1 otherwise. $\mathbf { X } ^ { ( t ) }$ denotes the concatenation of the weighted   
+124 local models at round $t$ , i.e., $\mathbf { X } ^ { ( t ) } = \left[ w _ { 1 } ^ { \prime } x _ { 1 } ^ { ( t ) } , \ldots , w _ { N } ^ { \prime } x _ { N } ^ { ( t ) } \right] ^ { \top } \in \mathbb { R } ^ { N \times d }$ . Finally, the server broadcasts   
+125 the updated global model $x ^ { ( t + 1 ) }$ to the users for the next round.
+
+Threat Model. Similar to the prior works on secure aggregation as [4, 15, 31], we consider the honest-but-curious model. All participants follow the protocol honestly in this model, but try to learn as much as possible about the users. At each round, the privacy of individual model $x _ { i } ^ { ( t ) }$ in (2) is protected by secure aggregation such that the server only learns the aggregated model $\textstyle \sum _ { i \in S ^ { ( t ) } } w _ { i } ^ { \prime } x _ { i } ^ { ( t ) }$
+
+# 3.2 Multi-round Secure Aggregation
+
+32 Conventional secure aggregation protocols only consider the privacy guarantees over a single training 33 round. While secure aggregation protocols have provable privacy guarantees at any single round, 4 in the sense that no information is leaked beyond the aggregate model at each round, the privacy 35 guarantees do not extend to attacks that span multiple training rounds. Specifically, by using the 36 aggregate models and participation information across multiple rounds, an individual model may be reconstructed. For instance, consider the following user participation strategy across three training 38 rounds, $\pmb { p } ^ { ( 1 ) } = [ 1 , 1 , 0 ] ^ { \top }$ , $\pmb { p } ^ { ( 2 ) } = [ 0 , 1 , 1 ] ^ { \top }$ , and $\pmb { p } ^ { ( 3 ) } = [ 1 , \bar { 0 } , 1 ] ^ { \top }$ . Assume a scenario where the local 9 updates do not change significantly over time (e.g., models start to converge, or the server fixes the global model over consecutive rounds), i.e., $x _ { i } = x _ { i } ^ { ( t ) }$ for all $i \in [ 3 ]$ and $t \in [ 3 ]$ . Then, the server can single out individual model, e.g., $\pmb { x } _ { 1 } = ( \pmb { x } ^ { ( 1 ) } + \pmb { x } ^ { ( 3 ) } - \pmb { x } ^ { ( 2 ) } ) / 2$ . Similarly, the server can single out all 2 individual models $x _ { i }$ , even if a secure aggregation protocol is employed at each round.
+
+143 In this paper, we study secure aggregation protocols with long-term privacy guarantees (which we   
+144 term multi-round secure aggregation) for the cross-device FL setup which has not been studied before.   
+145 We assume that user $i \in [ N ]$ drops from the protocol at each round with probability $p _ { i }$ . $\mathcal { U } ^ { ( t ) }$ denotes   
+146 the index set of available users at round $t$ and ${ \pmb u } ^ { ( t ) } \in \{ 0 , 1 \} ^ { N }$ is a vector indicating the available users   
+147 such that $\{ { \pmb u } ^ { ( t ) } \} _ { j } = \mathbb { 1 } \{ j \in { \mathcal { U } } ^ { ( t ) } \}$ , where $\{ \pmb { u } \} _ { j }$ is $j$ -th entry of $\pmb { u }$ and $\mathbb { 1 } \{ \cdot \}$ is the indicator function.   
+148 The server selects $K$ users from $\mathcal { U } ^ { ( t ) }$ , if $\vert \mathcal { U } ^ { ( t ) } \vert \ge K$ , based on the history of selected users in previous   
+149 rounds. If $\vert \mathcal { U } ^ { ( t ) } \vert < K$ , the server skips this round. The local models of the selected users are then   
+150 aggregated via a secure aggregation protocol (i.e., by communicating masked models), at the end of   
+151 which the server learns the aggregate of the local models of the selected users. Our goal is to design a   
+152 user selection algorithm $\mathcal { A } ^ { ( \bar { t } ) ^ { } } : \{ 0 , 1 \} ^ { t \times N } \times \{ 0 , 1 \} ^ { N } \to \{ 0 , 1 \} ^ { N } ,$ ,
+
+$$
+\begin{array} { r } { \mathcal { A } ^ { ( t ) } \big ( \mathbf { P } ^ { ( t ) } , \boldsymbol { u } ^ { ( t ) } \big ) = \boldsymbol { p } ^ { ( t ) } \ \mathrm { s u c h ~ t h a t } \ \| \boldsymbol { p } ^ { ( t ) } \| _ { 0 } \in \{ 0 , K \} , } \end{array}
+$$
+
+153 to prevent the potential information leakage over multiple rounds, where $\pmb { p } ^ { ( t ) } \in \{ 0 , 1 \} ^ { N }$ is the   
+154 participation vector defined in (2), $\| { \boldsymbol { x } } \| _ { 0 }$ denotes the $L _ { 0 }$ -“norm” of a vector $_ x$ and $K$ denotes the   
+155 number of selected users. We note that $\mathcal { A } ^ { ( t ) }$ can be a random function. $\mathbf { P } ^ { ( t ) }$ is a matrix representing   
+156 the user participation information up to round $t$ , and is termed the participation matrix, given by
+
+$$
+\mathbf { P } ^ { ( t ) } = \left[ { p ^ { ( 0 ) } , p ^ { ( 1 ) } , \ldots , p ^ { ( t - 1 ) } } \right] ^ { \top } \in \{ 0 , 1 \} ^ { t \times N } .
+$$
+
+157 Key Metrics. A multi-round secure aggregation protocol can be represented by $\mathcal { A } = \{ \mathcal { A } ^ { ( t ) } \} _ { t \in [ J ] }$   
+158 where $\mathcal { A } ^ { ( t ) }$ is the user selection algorithm at round $t$ defined in (3) and $J$ is the total number of rounds.   
+159 The inputs of $\mathcal { A } ^ { ( t ) }$ are a random vector $\mathbf { \Omega } _ { \pmb { u } } ( t )$ , which indicates the available users at round $t$ , and the   
+160 participation matrix $\mathbf { P } ^ { ( t ) }$ defined in (4) which can be a random matrix. Given the participation matrix   
+161 $\bar { \mathbf { p } } ( J )$ , we evaluate the performance of the corresponding multi-round secure aggregation protocol   
+162 through the following metrics.
+
+1. Multi-round Privacy Guarantee. The secure aggregation protocols ensure that the server can only learn the sum of the local models of some users in each single round, but they do not consider what the server can learn over the long run. Our multi-round privacy definition extends the guarantees of the secure aggregation protocols from one round to all rounds by requiring that the server can only learn a sum of the local models even if the server exploits the aggregate models of all rounds. That is, our multi-round privacy guarantee is a natural extension of the privacy guarantee provided by the secure aggregation protocols considering a single training round.
+
+170 Specifically, a multi-round privacy guarantee $T$ requires that any non-zero partial sum of the   
+171 local models that the server can reconstruct, through any linear combination $\mathbf { X } ^ { \top } \mathbf { P } ^ { ( J ) ^ { \top } } z$ , where   
+172 $z \in \mathbb { R } ^ { J } \setminus \{ \mathbf { 0 } \}$ , must be of the form1
+
+$$
+{ { \bf X } ^ { \top } { \bf P } ^ { ( J ) } } ^ { \top } z = \sum _ { i \in [ n ] } a _ { i } \sum _ { j \in S _ { i } } x _ { j } = a _ { 1 } \sum _ { j \in S _ { 1 } } x _ { j } + a _ { 2 } \sum _ { j \in S _ { 2 } } x _ { j } + \cdot \cdot \cdot + a _ { n } \sum _ { j \in S _ { n } } x _ { j } ,
+$$
+
+where $| S _ { i } | \ge T , a _ { i } \ne 0 , \forall i \in [ n ]$ and $n \in \mathbb { Z } ^ { + }$ . Here all the sets $S _ { i }$ , the number of sets $n$ , and each $a _ { i }$ could all depend on $z$ . In equation (5), we consider the worst-case scenario, where the local models do not change over the rounds. That is, $\mathbf { X } ^ { ( t ) } = \mathbf { X }$ , $\forall t \in [ J ]$ . Intuitively, this guarantee ensures that the best that the server can do is to reconstruct a partial sum of $T$ local models which corresponds to the case where $n = 1$ . When $T \geq 2$ , this condition implies that the server cannot get any user model from the aggregate models of all training rounds (the best it can obtain is the sum of two local models).
+
+Remark 1. (Weaker Privacy Notion). It is worth noting that, a weaker privacy notion would require that $\Vert \mathbf { P } ^ { ( J ) ^ { \top } } z \Vert _ { 0 } \geq T$ when $\mathbf { P } ^ { ( J ) ^ { \top } } z \neq \mathbf { 0 }$ . When $T = 2$ , this definition requires that the server cannot reconstruct any individual model (the best it can do is to obtain a linear combination of two local models). This notion, however, allows constructions in the form of $a x _ { i } + b x _ { j }$ for any $a , b \in \mathbb { R } \setminus \{ 0 \}$ . When $a \gg b$ , however, this is almost the same as recovering $x _ { i }$ perfectly, hence this privacy criterion is weaker than that of (5).
+
+Remark 2. (Multi-round Privacy of Random Selection). In Section 6, we empirically show that a random selection strategy in which $K$ available users are selected uniformly at random at each round does not ensure multi-round privacy even with respect to the weaker definition of Remark 1. Specifically, the local models can be reconstructed within a number of rounds that is linear in $N$ . We also show theoretically in Appendix $_ \mathrm { H }$ that when $\operatorname* { m i n } ( N - K , K ) \ge c N$ , where $c > 0$ is a constant, then the probability that the server can reconstruct all local models after $N$ rounds is
+
+192 193 scheme in which the users are selected in an i.i.d fashion according to Bern( 𝐾𝑁 (1−𝑝) ) at least $1 - 2 e ^ { - c ^ { \prime } N }$ for a constant $c ^ { \prime }$ that depends on $c$ . Finally, we show that a random selection reveals all   
+194 local models after $N$ rounds with probability that converges to 1 exponentially fast.
+
+Remark 3. (Worst-Case Assumption). In (5), we considered the worst-case assumption where the models do not change over time. When the local models change over rounds, the multi-round privacy guarantee becomes even stronger as the number of unknowns increases. In Fig. 1 and Appendix H, we empirically show that the conventional secure aggregation schemes leak extensive information of training data even in the realistic settings where the models change over the rounds.
+
+0 2. Aggregation Fairness Gap. The average aggregation fairness gap quantifies the largest gap   
+1 between any two users in terms of the expected relative number of rounds each user has participated   
+02 in training. Formally, the average aggregation fairness gap is defined as follows
+
+$$
+F = \operatorname* { m a x } _ { i \in [ N ] } \operatorname* { l i m } _ { J  \infty } \underset { J } { \operatorname* { s u p } } \frac { 1 } { J } \mathbb { E } \bigg [ \sum _ { t = 0 } ^ { J - 1 } \mathbb { 1 } \big \{ \{ p ^ { ( t ) } \} _ { i } = 1 \big \} \bigg ] - \operatorname* { m i n } _ { i \in [ N ] } \operatorname* { l i m } _ { J  \infty } \frac { 1 } { J } \mathbb { E } \bigg [ \sum _ { t = 0 } ^ { J - 1 } \mathbb { 1 } \big \{ \{ p ^ { ( t ) } \} _ { i } = 1 \big \} \bigg ] ,
+$$
+
+203 where $\{ \pmb { p } ^ { ( t ) } \} _ { i }$ is $i$ -th entry of the vector $\pmb { p } ^ { ( t ) }$ and the expectation is over the randomness of the user   
+204 selection algorithm $\mathcal { A }$ and the user availability. The main intuition behind this definition is that   
+205 when $F = 0$ , all users participate on average on the same number of rounds. This is important to   
+206 take the different users into consideration equally and our experiments show that the accuracy of   
+207 the schemes with small $F$ are much higher than the schemes with high $F$ .
+
+8 3. Average Aggregation Cardinality. The aggregation cardinality quantifies the expected number of models to be aggregated per round. Formally, it is defined as
+
+$$
+C = \operatorname* { l i m } _ { J  \infty } \operatorname* { i n f } _ { } \frac { \mathbb { E } \big [ \sum _ { t = 0 } ^ { J - 1 } \| p ^ { ( t ) } \| _ { 0 } \big ] } { J } ,
+$$
+
+where the expectation is over the randomness in $\mathcal { A }$ and the user availability. Intuitively, less number of rounds are needed to converge as more users participate in the training. In fact, as we show in Section 5.2, $C$ directly controls the convergence rate.
+
+# 3.3 Baseline Schemes
+
+In this subsection, we introduce three baseline schemes for multi-round secure aggregation.
+
+5 Random Selection. In this scheme, at each round, the server selects $K$ users at random from the set   
+6 of available users if this is possible.
+
+Random Weighted Selection. This scheme is a modified version of random selection to reduce $F$ when the dropout probabilities of the users are not equal. Specifically, $K$ users are selected at random from the available users with the minimum frequency of participation in the previous rounds.
+
+User Partitioning (Grouping). In this scheme, the users are partitioned into $G = N / K$ equal-sized groups denoted as $\mathcal { G } _ { 1 } , \mathcal { G } _ { 2 } , \cdots , \mathcal { G } _ { G }$ . At each round, the server selects one of the groups if none of the users in this group has dropped out. If multiple groups are available, to reduce the aggregation fairness gap, the server selects a group including a user with the minimum frequency of participation in previous rounds. If no group is available, the server skips this round.
+
+# 225 4 Proposed Scheme: Multi-RoundSecAgg
+
+In this section, we present Multi-RoundSecAgg, which has two components as follows.
+
+• The first component designs a family of sets of users that satisfy the multi-round privacy requirement. The inputs of the first component are the number of users $( N )$ , the number of selected users at each round $( K )$ , and the desired multi-round privacy guarantee $( T )$ . The output is a family of sets of $K$ users satisfying the multi-round privacy guarantee $T$ , termed as a privacy-preserving family. This family is represented by a matrix $\mathbf { B }$ , where the rows are the characteristic vectors of these user sets. • The second component selects a set from this designed family to satisfy the fairness guarantee. The inputs to the second component are the family $\mathbf { B }$ , the set of available users at round $t$ , $\mathcal { U } ^ { ( t ) }$ , and the frequency of participation of each user. The output is the set of users that will participate at round $t$ .
+
+235 We now describe these two components in detail.
+
+Component 1 (Batch Partitioning (BP) of the users to guarantee multi-round privacy). The first component designs a family of $R _ { \mathrm { B P } }$ sets, where $R _ { \mathrm { B P } }$ is the size of the set, satisfying the multiround privacy requirement $T$ . We denote the $R _ { \mathrm { B P } } \times N$ binary matrix corresponding to these sets by $\mathbf { B } = [ \pmb { b } _ { 1 } , \cdots , \pmb { b } _ { R _ { \mathrm { B P } } } ] ^ { \top }$ , where $\| \pmb { b } _ { i } \| _ { 0 } = K , \forall i \in \mathrm { ~ [ } R _ { \mathrm { B P } } ]$ . That is, the rows of $\mathbf { B }$ are the characteristic vectors of those sets. The main idea of our scheme is to restrict certain sets of users of size $T$ , denoted as batches, to either participate together or not participate at all. This guarantees a multi-round privacy $T$ as we show in Section 5.
+
+To construct a family of sets with this property, the users are first partitioned into $N / T$ batches. At any given round, either all or none of the users of a particular batch participate in training. The server can choose $K / T$ batches to participate in training, provided that all users in any given selected batch are available. Since there are $\binom { N / T } { K / T }$ possible sets with this property, then the size of this privacy-preserving family of sets is given by $R _ { \mathrm { B P } } { \stackrel { \mathrm { d e f } } { = } } { \binom { N / T } { K / T } } ^ { 2 }$ .
+
+In the extreme case of $T = 1$ , this strategy specializes to random selection where the server can choose any $K$ possible users. In the other extreme case of $T = K$ , this strategy specializes to the partitioning strategy where there are $N / K$ possible sets. We next provide an example to illustrate the construction of $\mathbf { B }$ .
+
+Example 1 $( N = 8 , K = 4 , T = 2 )$ . In this example, the users are partitioned into 4 batches as $\mathcal { G } _ { 1 } = \{ 1 , 2 \} , \mathcal { G } _ { 2 } = \{ 3 , 4 \} , \mathcal { G } _ { 3 } =$
+
+$$
+\mathbf B = \left[ \begin{array} { l l l l l l l l } { 1 } & { 1 } & { 1 } & { 1 } & { 1 } & { 0 } & { 0 } & { 0 } \\ { 1 } & { 1 } & { 0 } & { 0 } & { 1 } & { 1 } & { 1 } & { 0 } & { 0 } \\ { 1 } & { 1 } & { 0 } & { 0 } & { 0 } & { 0 } & { 1 } & { 1 } & { 1 } \\ { 0 } & { 0 } & { 1 } & { 1 } & { 1 } & { 1 } & { 1 } & { 1 } & { 0 } \\ { 0 } & { 0 } & { 1 } & { 1 } & { 1 } & { 0 } & { 0 } & { 1 } & { 1 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { 1 } & { 1 } & { 1 } & { 1 } \end{array} \right]
+$$
+
+Figure 2: Example of our construction with $N = 8$ , $K = 4$ and $T = 2$ .
+
+$\{ 5 , 6 \}$ and $\mathcal { G } _ { 4 } = \{ 7 , 8 \}$ as given in Fig. 2. The server can choose any two batches out of these 4 batches, hence we have $\begin{array} { r } { R _ { B P } = { \binom { 4 } { 2 } } = 6 } \end{array}$ possible sets. This ensures a multi-round privacy $T = 2$ .
+
+Component 2 (Available batch selection to guarantee fairness). At round $t$ , user $i \in [ N ]$ is   
+availaof useround rticipate round , and th n the protocolis denoted by  frequencies o $1 - p _ { i } \in ( 0 , 1 ]$ ncy of participationof available users at, the server selects $i$ $t$ $\begin{array} { r } { f _ { i } ^ { ( t ) } { \stackrel { \mathrm { d e f } } { = } } \sum _ { j = 0 } ^ { t - 1 } { \mathbb { 1 } } \left\{ \{ p ^ { ( j ) } \} _ { i } = 1 \right\} } \end{array}$ $t$ $\mathcal { U } ^ { ( t ) }$ $\boldsymbol { f } ^ { ( t - 1 ) } = ( f _ { 1 } ^ { ( t - 1 ) } , \cdot \cdot \cdot , f _ { N } ^ { ( t - 1 ) } )$   
+$K$ users. To do so, the server first finds the submatrix of $\mathbf { B }$ denoted by $\mathbf { B } ^ { ( t ) }$ corresponding to $\mathcal { U } ^ { ( t ) }$ .   
+Specifically, the $i .$ -th row of $\mathbf { B }$ denoted by $ { \boldsymbol { b } } _ { i } ^ { \top }$ is included in $\mathbf { B } ^ { ( t ) }$ provided that $\operatorname { s u p p } ( b _ { \mathrm { i } } ) \subseteq \mathcal { U } ^ { ( t ) }$ . If   
+$\mathbf { B } ^ { ( t ) }$ is an empty matrix, then the server skips this round. Otherwise, the server selects a row from $\mathbf { B } ^ { ( t ) }$   
+uniformly at random if $p _ { i } = p , \forall i \in [ N ]$ . If the users have different $p _ { i }$ , the server selects a row from   
+$\mathbf { B } ^ { ( t ) }$ that includes the user with the minimum frequency of participation $\ell _ { \mathrm { m i n } } ^ { ( t - 1 ) } \stackrel { \mathrm { d e f } } { = } \mathrm { a r g } \operatorname* { m i n } _ { i \in \mathcal { U } ^ { ( t ) } } f _ { i } ^ { ( t - 1 ) }$ (𝑡 ) 𝑓 (𝑡 −1)𝑖 .   
+If there are many such rows, then the server selects one of them uniformly at random.
+
+Remark 4. (Necessity of the Second Component). The second component is necessary to guarantee that the aggregation fairness gap goes to zero as we show in Theorem 1 and Section 6.
+
+Overall, the algorithm first designs a privacy-preserving family of sets to ensure the multi-round privacy guarantee $T$ . Then specific sets are selected from this family to ensure fairness. We describe the two components of Multi-RoundSecAgg in detail in Algorithm 1 and Algorithm 2 in Appendix D.
+
+# 5 Theoretical Results
+
+In this section, we provide the theoretical guarantees of Multi-RoundSecAgg in Section 5.1 and the convergence analysis of Multi-RoundSecAgg in Section 5.2.
+
+# 5.1 Theoretical Guarantees of Multi-RoundSecAgg
+
+In this subsection, we establish the theoretical guarantees of Multi-RoundSecAgg in terms of the multi-round privacy guarantee, the aggregation fairness gap and the average aggregation cardinality.
+
+78 Theorem 1. Multi-RoundSecAgg with parameters $N , K , T$ ensures a multi-round privacy guarantee   
+79 of 𝑇, an aggregation fairness gap $F = 0$ , and an average aggregation cardinality given by
+
+$$
+C = K \left( 1 - \sum _ { i = N / T - K / T + 1 } ^ { N / T } { \binom { N / T } { i } } q ^ { i } ( 1 - q ) ^ { N / T - i } \right) ,
+$$
+
+1 We provide the proof of Theorem 1 in Appendix A.
+
+Remark 5. (Trade-off between “Multi-round Privacy Guarantee” and “Average Aggregation Cardinality”). Theorem 1 indicates a trade-off between the multi-round privacy and the average aggregation cardinality since as $T$ increases, $C$ decreases which slows down the convergence as we show in Sec. 5.2. We show this trade-off in Fig. 3.
+
+Remark 6. (Necessity of Batch Partitioning (BP)). We show that any strategy that satisfies the privacy guarantee in Equation (5) must have a batch partitioning structure, and for given $N , K , T , K \le N / 2$ , the largest number of distinct user sets in any strategy is at most $\binom { N / T } { K / T }$ , which is achieved in our design in Section 4. We provide the proof in Appendix C.
+
+Remark 7. (Non-linear Reconstructions of Aggregated Models). The privacy criterion in Eq. (5) considers linear reconstructions of the aggregated models. One may also consider more general non-linear reconstructions. The long-term privacy guarantees of batch partitioning hold even under such reconstructions as the users in the same batch always participate together or do not participate at all. Hence, the server cannot separate individual models within the same batch even through non-linear operations.
+
+# 5.2 Convergence Analysis of Multi-RoundSecAgg
+
+For convergence analysis of Multi-RoundSecAgg, we first introduce a few common assumptions [23, 39].
+
+Assumption 1. $L _ { 1 } , \dots , L _ { N }$ in (1) are all $\rho$ -smooth: for all a, $\pmb { b } \in \mathbb { R } ^ { d }$ and $i \in [ N ]$ , $L _ { i } ( a ) \leq L _ { i } ( b ) + ( a -$ $\begin{array} { r } { \pmb { b } ) ^ { \top } \nabla L _ { i } ( \pmb { b } ) + \frac { \rho } { 2 } \| \pmb { a } - \pmb { b } \| ^ { 2 } } \end{array}$ .
+
+Assumption 2. $L _ { 1 } , \dots , L _ { N }$ in (1) are all $\mu$ -strongly convex: for all $a , b \in \mathbb { R } ^ { d }$ and $i \in [ N ]$ , $L _ { i } ( a ) \ \geq$ $\begin{array} { r } { L _ { i } ( b ) + ( a - b ) ^ { \top } \nabla L _ { i } ( b ) + \frac { \mu } { 2 } \| a - b \| ^ { 2 } } \end{array}$ .
+
+![](images/4b06ada298d1deefb6f48b19a75f8b5499036644959e55b0be1d80c85ea2eb22.jpg)  
+Figure 3: An illustration of the trade-off between the multi-round privacy guarantee $T$ and the average aggregation cardinality $C$ . In this example, $N = 1 2 0$ and $K = 1 2$ .
+
+Assumption 3. Let $\xi _ { i } ^ { ( t ) }$ be a sample uniformly selected from the dataset $\mathcal { D } _ { i }$ . The variance of the stochastic gradients at each user is bounded, i.e., $\mathbb { E } \| \nabla L _ { i } ( { \boldsymbol x } _ { i } ^ { ( t ) } , { \boldsymbol \xi } _ { i } ^ { ( t ) } ) - \nabla L _ { i } ( { \boldsymbol x } _ { i } ^ { ( t ) } ) \| ^ { 2 } \leq \sigma _ { i } ^ { 2 }$ for $i \in [ N ]$
+
+Assumption 4. The expected squared norm of the stochastic gradients is uniformly bounded, i.e., $\mathbb { E } \| \nabla L _ { i } \bar { ( } x _ { i } ^ { ( t ) } , \xi _ { i } ^ { ( t ) } ) \| ^ { 2 } \le \bar { G } ^ { 2 }$ for all $i \in [ N ]$ .
+
+We now state the convergence guarantees of Multi-RoundSecAgg.
+
+Theorem 2. Consider a $F L$ setup with $N$ users to train a machine learning model from (1). Assume $K$ users are selected by Multi-RoundSecAgg with average aggregation cardinality $C$ defined in (7) to update the global model from (2), and all users have the same dropout rate, hence Multi-RoundSecAgg selects a random set of $K$ users uniformly from the set of available user sets at each round. Then, the following is satisfied
+
+$$
+\mathbb { E } [ L ( x ^ { ( J ) } ) ] - L ^ { * } \leq \frac { \rho } { \gamma + \frac { C } { K } E J - 1 } \left( \frac { 2 ( \alpha + \beta ) } { \mu ^ { 2 } } + \frac { \gamma } { 2 } \mathbb { E } \| x ^ { ( 0 ) } - x ^ { * } \| ^ { 2 } \right) ,
+$$
+
+$$
+\begin{array} { r } { \alpha = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \sigma _ { i } ^ { 2 } + 6 \rho \Gamma + 8 ( E - 1 ) ^ { 2 } G ^ { 2 } , \beta = \frac { 4 ( N - K ) E ^ { 2 } G ^ { 2 } } { K ( N - 1 ) } , \Gamma = L ^ { * } - \sum _ { i = 1 } ^ { N } L _ { i } ^ { * } , a n d \gamma = \operatorname* { m a x } \left\{ \frac { 8 \rho } { \mu } , E \right\} } \end{array}
+$$
+
+316 We provide the proof of Theorem 2 in Appendix B.
+
+Remark 8. (The average aggregation cardinality controls the convergence rate.) Theorem 2 shows how the average aggregation cardinality affects the convergence. When the average aggregation cardinality is maximized, i.e., $C = K$ , the convergence rate in Theorem 2 equals that of the random selection algorithm provided in Theorem 3 of [23]. In (8), we have the additional term $E$ (number of local epochs) in front of $J$ compared to Theorem 3 of [23] as we use global round index $t$ instead of using step index of local SGD. As the average aggregation cardinality decreases, a greater number of training rounds is required to achieve the same level of accuracy.
+
+324 Remark 9. (General Convex and Non-Convex Convergence Rates). Theorem 2 considers the   
+325 strongly-convex case, but we consider the general convex and the non-convex cases in Appendix I.
+
+Remark 10. (Different Dropout Rates). When the dropout probabilities of the users are not the same, characterizing the convergence guarantees of Multi-RoundSecAgg is challenging. This is due to the fact that batch selection based on the frequency of participation breaks the conditional unbiasedness of the user selection, which is required for the convergence guarantee. In experiments, however, we empirically show that Multi-RoundSecAgg guarantees the convergence with different dropout rates.
+
+# 6 Experiments
+
+Our experiments consist of two parts. We first numerically demonstrate the performance of MultiRoundSecAgg compared to the baselines of Section 3.3 in terms of the key metrics of Section 3.2. Next, we implement convolutional neural networks (CNNs) for image classification with MNIST [21], CIFAR-10, and CIFAR-100 [20] to investigate how the key metrics affect the test accuracy.
+
+Setup. We consider a FL setting with $N = 1 2 0$ users, where the server aims to choose $K = 1 2$ users at every round. We study two settings for partitioning the CIFAR-100 dataset across the users.
+
+• IID Setting. 50000 training samples are shuffled and partitioned uniformly across $N = 1 2 0$ users. • Non-IID Setting. We distribute the dataset using a Dirichlet distribution [13], which samples $\mathbf { d } _ { c } \sim \mathrm { D i r } ( \beta = 0 . 5 )$ which specifying the prior class distribution over 100 classes, and allocate a portion $d _ { c , i }$ of the class $c$ to user $i$ . The parameter $\beta$ controls the heterogeneity of the distributions at each user, where $\beta \to \infty$ results in IID setting.
+
+We implement a VGG-11 [29], which is sufficient for our needs, as our goal is to evaluate various schemes, not to achieve the best accuracy. The hyperparameters are provided in Appendix F.
+
+Modeling dropouts. To model heterogeneous system, users have different dropout probability $p _ { i }$ selected from $\{ 0 . 1 , 0 . 2 , 0 . 3 , 0 . 4 , 0 . 5 \}$ . At each round, user $i \in [ N ]$ drops with probability $p _ { i }$ .
+
+Implemented Schemes. For the benchmarks, we implement the three baselines introduced in Sec. 3.3, referred to as Random, Weighted Random, and Partition. For Multi-RoundSecAgg, we construct three privacypreserving families with different target multi-round privacy guarantees, $T = 6$ , $T = 4$ , and $T = 3$ which we refer to as Multi-RoundSecAgg $( T \ = \ 6 )$ ), MultiRoundSecAgg $( T = 4 )$ ), and Multi-RoundSecAgg $( T =$
+
+<table><tr><td>Scheme</td><td>Family size (= R)</td></tr><tr><td>Random selection</td><td>~1016</td></tr><tr><td>Weighted random selection</td><td>~1016</td></tr><tr><td>User partition</td><td>10</td></tr><tr><td>Multi-RoundSecAgg,T=6</td><td>190</td></tr><tr><td>Multi-RoundSecAgg,T=4</td><td>4060</td></tr><tr><td>Multi-RoundSecAgg,T=3</td><td>91389</td></tr></table>
+
+Table 1: Family size with $N = 1 2 0$ , $K = 1 2$
+
+3), respectively. One can view the Random and Partition as extreme cases of Multi-RoundSecAgg with $T = 1$ and $T = K$ , respectively. Table 1 summarizes the family size $R$ defined in Section 4.
+
+Key Metrics. To numerically demonstrate the performance of the six schemes in terms of the key metrics defined in Sec. 3.2, at each round, we measure the following metrics.
+
+• For the multi-round privacy guarantee, we measure the number of models in the partial sum that the server can reconstruct, which is given by $\begin{array} { r }  T ^ { ( t ) } : = \operatorname* { m i n } _ { z \in \mathbb { R } ^ { J } \} \| z ^ { \top } { \bf P } ^ { ( t ) } \| _ { 0 } } \end{array}$ , s.t. $\bar { \mathbf { P } ^ { ( t ) } } ^ { \top } z \neq \mathbf { 0 }$ . This corresponds to the weaker privacy definition of Remark 1. We use this weaker privacy definition as the random selection and the random weighted selection strategies provide the worst privacy guarantee even with this weaker definition, as demonstrated later. On the other hand, MultiRoundSecAgg provides better privacy guarantees with both the strong and the weaker definitions. • For the aggregation fairness gap, we measure the instantaneous fairness gap, $\begin{array} { r l } { F ^ { ( t ) } } & { { } : = } \end{array}$ max𝑖 ∈ [ 𝑁 ] 𝐹 (𝑡)𝑖 − $\begin{array} { r } { \operatorname* { m a x } _ { i \in [ N ] } \bar { F _ { i } ^ { ( t ) } } - \operatorname* { m i n } _ { i \in [ N ] } F _ { i } ^ { ( t ) } } \end{array}$ where $\begin{array} { r } { F _ { i } ^ { ( t ) } = \frac { 1 } { t + 1 } \sum _ { l = 0 } ^ { t } \mathbb { 1 } \big \{ \{ p ^ { ( l ) } \} _ { i } = 1 \big \} } \end{array}$ .
+
+• We measure the instantaneous aggregation cardinality as $\begin{array} { r } { C ^ { ( t ) } : = \frac { 1 } { t + 1 } \sum _ { l = 0 } ^ { t } \| \pmb { p } ^ { ( l ) } \| _ { 0 } } \end{array}$
+
+We demonstrate these key metrics in Figure 4. We make the following key observations.
+
+• Multi-RoundSecAgg achieves better multi-round privacy guarantee than both the random selection and random weighted selection strategies, while user partitioning achieves the best multi-round privacy guarantee, $T = K = 1 2$ . However, the partitioning strategy has the worst aggregation cardinality, which results in the lowest convergence rate as demonstrated later.
+
+• Figure 5 demonstrates the trade-off between the multi-round privacy guarantee $T$ and the average aggregation cardinality $C$ . Interestingly, Multi-RoundSecAgg when $T = 3$ or $T = 4$ achieves better multi-round privacy guarantee than both the random selection and the weighted random selection strategies while achieving almost the same average aggregation cardinality.
+
+![](images/152549e879570cea0e13e50b34b4cdbadc678f73db8855448f893588f4eb7d08.jpg)  
+Figure 4: The key metrics with $N = 1 2 0$ (number of users), $K = 1 2$ (number of selected users at each round).
+
+![](images/bc06b6995b08a5632d87e4b5aebb7abb09abda62fba56f6cae4ee5fd78dd9a21.jpg)  
+Figure 5: Trade-off between multi-round privacy and average aggregation cardinality with $N =$ 120, $K = 1 2$ .
+
+![](images/8ec0eebad5aae5a6325b8d51608e405818358d0c91afaaf3d8ee79fcf426bf9c.jpg)  
+Figure 6: Training rounds versus test accuracy of VGG11 in [29] on the CIFAR-100 with $N = 1 2 0$ and $K = 1 2$ .
+
+Remark 11. (Multi-round Privacy of Random and Weighted Random). The multi-round privacy guarantees of Random and Weighted Random drop sharply as shown in Fig. 4(a) as the participating matrix $\mathbf { P } ^ { ( t ) } \in \{ 0 , 1 \} ^ { t \times N }$ becomes full rank with high probability when $t \geq N$ , and hence the server can reconstruct the individual models by utilizing a pseudo inversion of the matrix $\mathbf { P } ^ { ( t ) }$ . More precisely, Theorem 3 in Appendix H shows this thresholding phenomenon, where the probability that the server can reconstruct individual models after certain number of rounds converges to 1 exponentially fast.
+
+Key Metrics versus Test Accuracy. To investigate how the key metrics affect the test accuracy, we measure the test accuracy of the six schemes in the two settings, the IID and the non-IID settings. Our results are demonstrated in Figure 6. We make the following key observations.
+
+• In the IID setting, the Multi-RoundSecAgg schemes show test accuracies that are comparable to the random selection and random weighted selection schemes while the Multi-RoundSecAgg schemes provide higher levels of privacy. Specifically, the Multi-RoundSecAgg schemes achieve $T = 3 , 4 , 6$ based on the privacy-preserving family design while the random selection and random weighted selection schemes have $T = 1$ , i.e., the server can learn an individual local model. • In the non-IID setting, Multi-RoundSecAgg not only outperforms the random selection scheme but also achieves a smaller aggregation fairness gap as demonstrated in Fig. 4(b). • In both IID and non-IID settings, the user partitioning scheme has the worst accuracy as its average aggregation cardinality is much smaller than the other schemes as demonstrated in Fig. 4(c).
+
+We also implement additional experiments on MNIST and CIFAR-10 datasets in Appendix E and present ablation study for various settings of $( N , K , T )$ in Appendix G
+
+# 7 7 Conclusion
+
+Partial user participation may breach user privacy in federated learning, even if secure aggregation is employed at every training round. To address this challenge, we introduced the notion of long-term privacy, which ensures that the privacy of individual models are protected over all training rounds. We developed Multi-RoundSecAgg, a structured user selection strategy that guarantees long-term privacy while taking into account the fairness in user selection and average number of participating users, and showed that Multi-RoundSecAgg provides a trade-off between long-term privacy and average number of participating users (hence the convergence rate). Our experiments on the CIFAR-100, CIFAR-10, and MNIST datasets on both the IID and non-IID settings show that Multi-RoundSecAgg achieves comparable accuracy to the random selection strategy (which does not ensure long-term privacy), while ensuring long-term privacy guarantees.
+
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