Tabular Representation Learning

Tabular foundation models (TFMs) increasingly rival tree ensembles, but their performance is often compute-inefficient: with standard affine scalar tokenization, each feature injects value variation through an essentially one-dimensional channel, and feature IDs/positional signals cannot increase within-feature value degrees of freedom, yielding weak early-layer value sensitivity and redundant hidden states. We present a unified tokenize-and-route framework for strong TFMs: RaBEL expands each scalar into compact localized RBF features (optionally exponent-gated) to improve conditioning and shallow-layer effective rank, while a reordered bidirectional block S->N->F aligns computation with the readout by aggregating cross-sample context before feature mixing and using attention pooling. Together, these changes yield LimiX-2M, a 2M-parameter model that outperforms larger TabPFN-v2 and TabICL baselines on widely used tabular benchmarks while reducing training and inference costs. These results highlight value-aware tokenization and readout-aligned routing as key levers for improving the accuracy--efficiency trade-off in TFMs. Model checkpoints and inference code are available at https://github.com/limix-ldm-ai/LimiX.

Real-world domains often contain heterogeneous tables whose headers vary while their underlying attribute semantics are shared, making it difficult to induce domain-specialized semantics from table-local evidence alone. Existing encoders model parts of this problem, but often underuse column-level value distributions and apply uniform objectives across attributes with different semantic roles. We propose NAVI, a segment-centric pretraining framework that treats each header-value pair as the unit for aggregating schema-level structural evidence and column-level distributional evidence. We realize this design through Masked Segment Modeling and Entropy-driven Segment Alignment, which jointly enforce structured header-value coupling and semantic alignment across stable and instance-specific attributes. Experiments on heterogeneous in-domain tables show improved reconstruction, semantic consistency, and downstream utility across evaluation settings overall.

Tabular data forms the backbone of high-stakes decision systems in finance, healthcare, and beyond. Yet industrial tabular datasets are inherently difficult: high-dimensional, riddled with missing entries, and rarely labeled at scale. While foundation models have revolutionized vision and language, tabular learning still leans on handcrafted features and lacks a general self-supervised framework. We present MaskTab, a unified pre-training framework designed specifically for industrial-scale tabular data. MaskTab encodes missing values via dedicated learnable tokens, enabling the model to distinguish structural absence from random dropout. It jointly optimizes a hybrid supervised pre-training scheme--utilizing a twin-path architecture to reconcile masked reconstruction with task-specific supervision--and an MoE-augmented loss that adaptively routes features through specialized subnetworks. On industrial-scale benchmarks, it achieves +5.04% AUC and +8.28% KS over prior art under rigorous scaling. Moreover, its representations distill effectively into lightweight models, yielding +2.55% AUC and +4.85% KS under strict latency and interpretability constraints, while improving robustness to distribution shifts. Our work demonstrates that tabular data admits a foundation-model treatment--when its structural idiosyncrasies are respected.

Tabular Foundation Models have recently established the state of the art in supervised tabular learning, by leveraging pretraining to learn generalizable representations of numerical and categorical structured data. However, they lack native support for unstructured modalities such as text and image, and rely on frozen, pretrained embeddings to process them. On established Multimodal Tabular Learning benchmarks, we show that tuning the embeddings to the task improves performance. Existing benchmarks, however, often focus on the mere co-occurrence of modalities; this leads to high variance across datasets and masks the benefits of task-specific tuning. To address this gap, we introduce MulTaBench, a benchmark of 40 datasets, split equally between image-tabular and text-tabular tasks. We focus on predictive tasks where the modalities provide complementary predictive signal, and where generic embeddings lose critical information, necessitating Target-Aware Representations that are aligned with the task. Our experimental results demonstrate that the gains from target-aware representation tuning generalize across both text and image modalities, several tabular learners, encoder scales, and embedding dimensions. MulTaBench constitutes the largest image-tabular benchmarking effort to date, spanning high-impact domains such as healthcare and e-commerce. It is designed to enable the research of novel architectures which incorporate joint modeling and target-aware representations, paving the way for the development of novel Multimodal Tabular Foundation Models.

Generative modelling is a demanding test of foundation models, because it requires robust, holistic representation learning for a given data modality, rather than optimisation for a supervised prediction target alone. While recent work on tabular foundation models has achieved remarkable progress in predictive modelling, generative tabular foundation models remain underexplored. Existing tabular foundation generators, in particular, have not yet consistently matched strong dataset-specific generators in synthetic data quality. A key reason is their insufficient alignment with the inter-feature dependency structure of tabular data, which can reflect underlying causal relationships. In this paper, we address this gap by introducing a novel tabular foundation model, $\textbf{TabFORGE}$, built on pretrained $\textbf{Tab}$ular $\textbf{FO}$undational $\textbf{R}$epresentations for $\textbf{GE}$neration. TabFORGE is designed to utilise transferable representations induced by a pretrained structure-aware feature encoder, which captures information useful for characterising inter-feature dependencies. It further decouples latent modelling from decoding through a two-stage design: we first pretrain a score-based diffusion transformer, and then pretrain a denoising-aligned decoder using the denoised latent embeddings. This design elegantly mitigates the distribution shifts in latent embeddings that typically arise between training and inference. We evaluate TabFORGE comprehensively against 22 benchmark methods on 45 real-world datasets. Our results show that TabFORGE effectively learns and leverages generalisable tabular representations, enabling efficient generation of high-quality synthetic tabular data, particularly with strong structural fidelity. Code is available at https://github.com/SilenceX12138/TabFORGE.

Foundation models have established unified representations for natural language processing, yet this paradigm remains largely unexplored for tabular data. Existing methods face fundamental limitations: LLM-based approaches lack retrieval-compatible vector outputs, whereas text embedding models often fail to capture tabular structure and numerical semantics. To bridge this gap, we first introduce the Tabular Embedding Benchmark (TabBench), a comprehensive suite designed to evaluate the tabular understanding capability of embedding models. We then propose TabEmbed, the first generalist embedding model that unifies tabular classification and retrieval within a shared embedding space. By reformulating diverse tabular tasks as semantic matching problems, TabEmbed leverages large-scale contrastive learning with positive-aware hard negative mining to discern fine-grained structural and numerical nuances. Experimental results on TabBench demonstrate that TabEmbed significantly outperforms state-of-the-art text embedding models, establishing a new baseline for universal tabular representation learning. Code and datasets are publicly available at https://github.com/qiangminjie27/TabEmbed and https://huggingface.co/datasets/qiangminjie27/TabBench.

Classic Network Intrusion Detection Systems (NIDS) often rely on manual feature engineering to extract meaningful patterns from network traffic data. However, this approach requires domain expertise and runs counter to the widely adopted principle of modern machine learning and neural networks: that models themselves should learn meaningful representations directly from data. We investigate whether tabular representation learning techniques can improve intrusion detection performance by automatically learning robust feature representations for NetFlow data. This paper presents a systematic evaluation of state-of-the-art representation learning methods on benchmark NetFlow datasets, comparing against traditional autoencoders and end-to-end transformer baselines. We evaluate learned representations using both supervised classifiers and unsupervised anomaly detectors, with comprehensive hyperparameter exploration for each combination. Our results reveal strong dataset-model dependency, with no single approach consistently dominating across all scenarios. For supervised classification, TabICL achieves the best performance on CIDDS, while autoencoders follow closely and tie with end-to-end transformer models for the best average rank across datasets. Supervised approaches substantially outperform unsupervised anomaly detection methods, where no single combination consistently dominates as optimal choices depend on the dataset. Cross-dataset transfer experiments demonstrate that learned representations can generalize across network environments with appropriate method and classifier selection. However, transfer performance varies substantially depending on the source-target dataset combination, indicating sensitivity to distributional differences between network environments.

Learning informative representations from tabular data in remote sensing and environmental science is challenging due to heterogeneity, scarce labels, and redundancy among features. We present ZAYAN (Zero-Anchor dYnamic feAture eNcoding), a self-supervised, feature-centric contrastive framework for tabular data. ZAYAN performs contrastive learning at the feature rather than sample level, removing the need for explicit anchor selection and any reliance on class labels, while encouraging a redundancy-minimized, disentangled embedding space. The framework has two modules: ZAYAN-CL, which pretrains feature embeddings via a zero-anchor contrastive objective with dynamic perturbations and masking, and ZAYAN-T, a Transformer that conditions on these embeddings for downstream classification. Across eight datasets, including six remote-sensing tabular benchmarks and two remote-sensing-driven flood-prediction tables from satellite and GIS products, ZAYAN achieves superior accuracy, robustness, and generalization over tabular deep learning baselines, with consistent gains under label scarcity and distribution shift. These results indicate that feature-level contrastive learning and dynamic feature encoding provide an effective recipe for learning from tabular sensing data.

Tabular foundation models aim to learn universal representations of tabular data that transfer across tasks and domains, enabling applications such as table retrieval, semantic search and table-based prediction. Despite the growing number of such models, it remains unclear which approach works best in practice, as existing methods are often evaluated under task-specific settings that make direct comparison difficult. To address this, we introduce TEmBed, the Tabular Embedding Test Bed, a unified benchmark for systematically evaluating tabular embeddings across four representation levels: cell, row, column, and table. Evaluating a diverse set of tabular representation learning models, we show that which model to use depends on the task and representation level. Our results offer practical guidance for selecting tabular embeddings in real-world applications and lay the groundwork for developing more general-purpose tabular representation models.

Table annotation is crucial for making web and enterprise tables usable in downstream NLP applications. Unlike textual data where learning semantically rich token or sentence embeddings often suffice, tables are structured combinations of columns wherein useful representations must jointly capture column's semantics and the inter-column relationships. Existing models learn by linearizing the 2D table into a 1D token sequence and encoding it with pretrained language models (PLMs) such as BERT. However, this leads to limited semantic quality and weaker generalization to unseen or rare values compared to modern LLMs, and degraded structural modeling due to 2D-to-1D flattening and context-length constraints. We propose TabEmb, which directly targets these limitations by decoupling semantic encoding from structural modeling. An LLM first produces semantically rich embeddings for each column, and a graph-based module over columns then injects relationships into the embeddings, yielding joint semantic-tructural representations for table annotation. Experiments show that TabEmb consistently outperforms strong baselines on different table annotation tasks. Source code and datasets are available at https://github.com/hoseinzadeehsan/TabEmb

Historical approaches to Table Representation Learning (TRL) have largely adopted the sequential paradigms of Natural Language Processing (NLP). We argue that this linearization of tables discards their essential geometric and relational structure, creating representations that are brittle to layout permutations. This paper introduces the Platonic Representation Hypothesis (PRH) for tables, positing that a semantically robust latent space for table reasoning must be intrinsically Permutation Invariant (PI). To ground this hypothesis, we first conduct a retrospective analysis of table-reasoning tasks, highlighting the pervasive serialization bias that compromises structural integrity. We then propose a formal framework to diagnose this bias, introducing two principled metrics based on Centered Kernel Alignment (CKA): (i) PI, which measures embedding drift under complete structural derangement, and (ii) rho, a Spearman-based metric that tracks the convergence of latent structures toward a canonical form as structural information is incrementally restored. Our empirical analysis quantifies an expected flaw in modern Large Language Models (LLMs): even minor layout permutations induce significant, disproportionate semantic shifts in their table embeddings. This exposes a fundamental vulnerability in RAG systems, in which table retrieval becomes fragile to layout-dependent noise rather than to semantic content. In response, we present a novel, structure-aware TRL encoder architecture that explicitly enforces the cognitive principle of cell header alignment. This model demonstrates superior geometric stability and moves towards the PI ideal. Our work provides both a foundational critique of linearized table encoders and the theoretical scaffolding for semantically stable, permutation invariant retrieval, charting a new direction for table reasoning in information systems.

Deep Clustering (DC) has emerged as a powerful tool for tabular data analysis in real-world domains like finance and healthcare. However, most existing methods rely on data-level statistical co-occurrence to infer the latent metric space, often overlooking the intrinsic semantic knowledge encapsulated in feature names and values. As a result, semantically related concepts like Flu' and Cold' are often treated as symbolic tokens, causing conceptually related samples to be isolated. To bridge the gap between dataset-specific statistics and intrinsic semantic knowledge, this paper proposes Tabular-Augmented Contrastive Clustering (TagCC), a novel framework that anchors statistical tabular representations to open-world textual concepts. Specifically, TagCC utilizes Large Language Models (LLMs) to distill underlying data semantics into textual anchors via semantic-aware transformation. Through Contrastive Learning (CL), the framework enriches the statistical tabular representations with the open-world semantics encapsulated in these anchors. This CL framework is jointly optimized with a clustering objective, ensuring that the learned representations are both semantically coherent and clustering-friendly. Extensive experiments on benchmark datasets demonstrate that TagCC significantly outperforms its counterparts.

Machine learning for tabular data remains constrained by poor schema generalization, a challenge rooted in the lack of semantic understanding of structured variables. This challenge is particularly acute in domains like clinical medicine, where electronic health record (EHR) schemas vary significantly. To solve this problem, we propose Schema-Adaptive Tabular Representation Learning, a novel method that leverages large language models (LLMs) to create transferable tabular embeddings. By transforming structured variables into semantic natural language statements and encoding them with a pretrained LLM, our approach enables zero-shot alignment across unseen schemas without manual feature engineering or retraining. We integrate our encoder into a multimodal framework for dementia diagnosis, combining tabular and MRI data. Experiments on NACC and ADNI datasets demonstrate state-of-the-art performance and successful zero-shot transfer to unseen schemas, significantly outperforming clinical baselines, including board-certified neurologists, in retrospective diagnostic tasks. These results validate our LLM-driven approach as a scalable, robust solution for heterogeneous real-world data, offering a pathway to extend LLM-based reasoning to structured domains.

Employee attrition presents a major challenge for organizations, increasing costs and reducing productivity. Predicting attrition accurately enables proactive retention strategies, but existing machine learning models often struggle to capture complex feature interactions in tabular HR datasets. While tree-based models such as XGBoost and LightGBM perform well on structured data, traditional encoding techniques like one-hot encoding can introduce sparsity and fail to preserve semantic relationships between categorical features. This study explores a hybrid approach by integrating SAINT (Self-Attention and Intersample Attention Transformer)-generated embeddings with tree-based models to enhance employee attrition prediction. SAINT leverages self-attention mechanisms to model intricate feature interactions. In this study, we explore SAINT both as a standalone classifier and as a feature extractor for tree-based models. We evaluate the performance, generalizability, and interpretability of standalone models (SAINT, XGBoost, LightGBM) and hybrid models that combine SAINT embeddings with tree-based classifiers. Experimental results show that standalone tree-based models outperform both the standalone SAINT model and the hybrid approaches in predictive accuracy and generalization. Contrary to expectations, the hybrid models did not improve performance. One possible explanation is that tree-based models struggle to utilize dense, high-dimensional embeddings effectively. Additionally, the hybrid approach significantly reduced interpretability, making model decisions harder to explain. These findings suggest that transformer-based embeddings, while capturing feature relationships, do not necessarily enhance tree-based classifiers. Future research should explore alternative fusion strategies for integrating deep learning with structured data.

Tabular data, widely used in various applications such as industrial control systems, finance, and supply chain, often contains complex interrelationships among its attributes. Data disentanglement seeks to transform such data into latent variables with reduced interdependencies, facilitating more effective and efficient processing. Despite the extensive studies on data disentanglement over image, text, or audio data, tabular data disentanglement may require further investigation due to the more intricate attribute interactions typically found in tabular data. Moreover, due to the highly complex interrelationships, direct translation from other data domains results in suboptimal data disentanglement. Existing tabular data disentanglement methods, such as factor analysis, CT-GAN, and VAE face limitations including scalability issues, mode collapse, and poor extrapolation. In this paper, we propose the use of a framework to provide a systematic view on tabular data disentanglement that modularizes the process into four core components: data extraction, data modeling, model analysis, and latent representation extrapolation. We believe this work provides a deeper understanding of tabular data disentanglement and existing methods, and lays the foundation for potential future research in developing robust, efficient, and scalable data disentanglement techniques. Finally, we demonstrate the framework's applicability through a case study on synthetic tabular data generation, showcasing its potential in the particular downstream task of data synthesis.

Numerical preprocessing remains a critical component of tabular deep learning, as the representation of continuous features can strongly affect downstream performance. We systematically study spline-based numerical encodings, including B-splines, M-splines, and integrated splines (I-splines), under uniform, quantile-based, target-aware, and learnable-knot placement. For the learnable variants, we adopt a differentiable knot parameterization that enables stable end-to-end optimization of knot locations jointly with the backbone. We evaluate these encodings on a diverse collection of public regression and classification datasets using MLP, ResNet, and FT-Transformer backbones, and compare them against common numerical preprocessing baselines. Our results show that the effectiveness of numerical encoding depends strongly on the task, encoding size, and backbone. For classification, piecewise-linear encoding (PLE) is the most robust choice overall, while spline-based encodings remain competitive. For regression, no single encoding dominates, with performance depending on the spline family and knot-placement strategy, and larger gains generally observed for MLP and ResNet than for FT-Transformer. Learnable-knot variants can be optimized stably but may substantially increase training cost. Overall, numerical encodings should therefore be assessed jointly in terms of predictive performance and computational overhead. The implementation is publicly available at https://github.com/mkumar73/tdl-numerical-encodings/.

Tabular data are central to biomedical research, from liquid biopsy and bulk and single-cell transcriptomics to electronic health records and phenotypic profiling. Unlike images or sequences, however, tabular datasets lack intrinsic spatial organization: features are treated as unordered dimensions, and their relationships must be inferred implicitly by the model. This limits the ability of vision architectures to exploit local structure and higher-order feature interactions in non-spatial biomedical data. Here we introduce Dynamic Feature Mapping (Dynomap), an end-to-end deep learning framework that learns a task-optimized spatial topology of features directly from data. Dynomap jointly optimizes feature placement and prediction through a fully differentiable rendering mechanism, without relying on heuristics, predefined groupings, or external priors. By transforming high-dimensional tabular vectors into learned feature maps, Dynomap enables vision-based models to operate effectively on unordered biomedical inputs. Across multiple clinical and biological datasets, Dynomap consistently outperformed classical machine learning, modern deep tabular models, and existing vector-to-image approaches. In liquid biopsy data, Dynomap organized clinically relevant gene signatures into coherent spatial patterns and improved multiclass cancer subtype prediction accuracy by up to 18%. In a Parkinson disease voice dataset, it clustered disease-associated acoustic descriptors and improved accuracy by up to 8%. Similar gains and interpretable feature organization were observed in additional biomedical datasets. These results establish Dynomap as a general strategy for bridging tabular and vision-based deep learning and for uncovering structured, clinically relevant patterns in high-dimensional biomedical data.

Although mechanism-based interpretability has generated an abundance of insight for discriminative network analysis, generative models are less understood -- particularly outside of image-related applications. We investigate how much of the causal circuitry found within image-related variational autoencoders (VAEs) will generalize to tabular data, as VAEs are increasingly used for imputation, anomaly detection, and synthetic data generation. In addition to extending a four-level causal intervention framework to four tabular and one image benchmark across five different VAE architectures (with 75 individual training runs per architecture and three random seed values for each run), this paper introduces three new techniques: posterior-calibration of Causal Effect Strength (CES), path-specific activation patching, and Feature-Group Disentanglement (FGD). The results from our experiments demonstrate that: (i) Tabular VAEs have circuits with modularity that is approximately 50% lower than their image counterparts. (ii) $β$-VAE experiences nearly complete collapse in CES scores when applied to heterogeneous tabular features (0.043 CES score for tabular data compared to 0.133 CES score for images), which can be directly attributed to reconstruction quality degradation (r = -0.886 correlation coefficient between CES and MSE). (iii) CES successfully captures nine of eleven statistically significant architecture differences using Holm--Šidák corrections. (iv) Interventions with high specificity predict the highest downstream AUC values (r = 0.460, p < .001). This study challenges the common assumption that architectural guidance from image-related studies can be transferred to tabular datasets.

Despite their dominance in vision and language, deep neural networks often underperform relative to tree-based models on tabular data. To bridge this gap, we incorporate five key inductive biases into deep learning: robustness to irrelevant features, axis alignment, localized irregularities, feature heterogeneity, and training stability. We propose LassoFlexNet, an architecture that evaluates the linear and nonlinear marginal contribution of each input via Per-Feature Embeddings, and sparsely selects relevant variables using a Tied Group Lasso mechanism. Because these components introduce optimization challenges that destabilize standard proximal methods, we develop a Sequential Hierarchical Proximal Adaptive Gradient optimizer with exponential moving averages (EMA) to ensure stable convergence. Across $52$ datasets from three benchmarks, LassoFlexNet matches or outperforms leading tree-based models, achieving up to a $10$% relative gain, while maintaining Lasso-like interpretability. We substantiate these empirical results with ablation studies and theoretical proofs confirming the architecture's enhanced expressivity and structural breaking of undesired rotational invariance.

Embeddings are a powerful way to enrich data-driven machine learning models with the world knowledge of large language models (LLMs). Yet, there is limited evidence on how to design effective LLM-based embedding pipelines for tabular prediction. In this work, we systematically benchmark 256 pipeline configurations, covering 8 preprocessing strategies, 16 embedding models, and 2 downstream models. Our results show that it strongly depends on the specific pipeline design whether incorporating the prior knowledge of LLMs improves the predictive performance. In general, concatenating embeddings tends to outperform replacing the original columns with embeddings. Larger embedding models tend to yield better results, while public leaderboard rankings and model popularity are poor performance indicators. Finally, gradient boosting decision trees tend to be strong downstream models. Our findings provide researchers and practitioners with guidance for building more effective embedding pipelines for tabular prediction tasks.

Tabular data have been playing a mostly important role in diverse real-world fields, such as healthcare, engineering, finance, etc. The recent success of deep learning has fostered many deep networks (e.g., Transformer, ResNet) based tabular learning methods. Generally, existing deep tabular machine learning methods are along with the two paradigms, i.e., in-learning and pre-learning. In-learning methods need to train networks from scratch or impose extra constraints to regulate the representations which nonetheless train multiple tasks simultaneously and make learning more difficult, while pre-learning methods design several pretext tasks for pre-training and then conduct task-specific fine-tuning, which however need much extra training effort with prior knowledge. In this paper, we introduce a novel deep Tabular Representation Corrector, TRC, to enhance any trained deep tabular model's representations without altering its parameters in a model-agnostic manner. Specifically, targeting the representation shift and representation redundancy that hinder prediction, we propose two tasks, i.e., (i) Tabular Representation Re-estimation, that involves training a shift estimator to calculate the inherent shift of tabular representations to subsequently mitigate it, thereby re-estimating the representations and (ii) Tabular Space Mapping, that transforms the above re-estimated representations into a light-embedding vector space via a coordinate estimator while preserves crucial predictive information to minimize redundancy. The two tasks jointly enhance the representations of deep tabular models without touching on the original models thus enjoying high efficiency. Finally, we conduct extensive experiments on state-of-the-art deep tabular machine learning models coupled with TRC on various tabular benchmarks which have shown consistent superiority.

While Deep Learning has demonstrated impressive results in applications on various data types, it continues to lag behind tree-based methods when applied to tabular data, often referred to as the last "unconquered castle" for neural networks. We hypothesize that a significant advantage of tree-based methods lies in their intrinsic capability to model and exploit non-linear interactions induced by features with categorical characteristics. In contrast, neural-based methods exhibit biases toward uniform numerical processing of features and smooth solutions, making it challenging for them to effectively leverage such patterns. We address this performance gap by using statistical-based feature processing techniques to identify features that are strongly correlated with the target once discretized. We further mitigate the bias of deep models for overly-smooth solutions, a bias that does not align with the inherent properties of the data, using Learned Fourier. We show that our proposed feature preprocessing significantly boosts the performance of deep learning models and enables them to achieve a performance that closely matches or surpasses XGBoost on a comprehensive tabular data benchmark.

Electronic health records (EHR) arrive masked. Clinicians order measurements selectively, and any patient table thus contains only a subset of the values that characterize the underlying physiological state. Prior masked modeling approaches on EHR data either impute the table before learning, represent missingness through a dedicated placeholder signal, or optimize solely for imputation, which limits the representations they learn for downstream clinical tasks and carries every unobserved entry through the encoder. We introduce AID-MAE, an Augmented-Intrinsic Dual-Masked Autoencoder that learns directly from incomplete tables by combining the intrinsic mask the record already carries with an augmented mask that hides a subset of observed values for reconstruction during pretraining. Neither type of masked entry enters the encoder, so attention operates only over what was observed. AID-MAE achieves consistent improvements over strong baselines across multiple clinical tasks on two datasets. Across experiments, we discuss that recovering the missing entries is not a prerequisite for learning and show that the representations learned carry clinical structure without supervision.