FEAT: A Linear-Complexity Foundation Model for Extremely Large Structured Data
Authors: Zhenghang Song, Tang Qian, Lu Chen, Yushuai Li, Zhengke Hu, Bingbing Fang, Yumeng Song, Junbo Zhao, +2 more
Abstract
Structured data is widely used in domains such as healthcare, finance, and scientific data management. Recent studies on structured data foundation models (SFMs) aim to support data analysis and mining tasks over such data, but still face scalability and generalization challenges when applied to real-world enterprise databases. First, many SFMs rely on full self-attention, which introduces an O(N^2) computational bottleneck and limits the number of tuples that can be processed jointly. Second, directly replacing attention with linear-complexity sequence models may conflict with the permutation-invariant nature of structured data, introducing artificial order bias and degrading representation quality. Moreover, models trained only on synthetic data may struggle to generalize to the heavy-tailed and heterogeneous distributions commonly found in real-world databases. To address these challenges, we propose FEAT, a linear-complexity foundation model for extremely large structured data. FEAT replaces quadratic attention with a multi-layer dual-axis encoding architecture. It integrates an adaptive-fusion bidirectional state-space model (AFBM) with convolutional gated linear attention (Conv-GLA), enabling cross-tuple contextualization in O(N) time while supporting permutation-invariant representation learning. To improve robustness under real-world data skewness, FEAT further adopts a hybrid structural causal pre-training pipeline with a robust reconstruction objective. Experiments on 12 real-world database benchmarks show that FEAT consistently outperforms representative SFMs on zero-shot tasks and scales linearly with structured-data sample length, achieving up to 50x faster inference latency.
Chain-of-thought and more broadly test-time compute are known to augment the expressive capabilities of language models and have led to major innovations in reasoning. Motivated by this success, this paper explores latent chain-of-thought as well as the impact of depth and looping for time-series and tabular data. We propose a recurrent scheme in which a structured-data transformer, after an initial forward pass, compresses its query-position hidden states into feedback tokens that are appended to the input and processed again, allowing multiple rounds of latent computation before prediction. We compare CoT models against a same-depth no-CoT baseline, a deeper baseline matched to the CoT model in effective depth, and a looped transformer with weight-tied recurrence but no additional chain-of-thought tokens. Across 36 datasets in time-series forecasting and tabular prediction, latent chain-of-thought improves over the baseline on 7/9 time-series datasets (+12.63% average gain) and 23/27 tabular datasets (+3.25% average gain), with CoT models performing best on average in both settings. We also show that the benefit of CoT extends to pretrained foundation models: applying latent CoT to nanoTabPFN, a small open-source tabular foundation model, improves its performance above the much larger TabPFN-v2 on TabArena. Together, these results demonstrate that chain-of-thought is a useful axis for scaling test-time compute for structured data.
Clinical risk prediction using longitudinal medical data supports individualized care. Self-supervised foundation models have emerged as a promising approach for leveraging large-scale unlabeled healthcare records. In natural language processing, scaling laws suggest that larger models achieve predictably lower pretraining losses, supporting the foundation model paradigm. However, for structured medical data, characterized by a limited vocabulary and sparse observations, whether increasing model size consistently improves downstream predictions is unclear, as most studies evaluate only a single model scale. In this study, we evaluated the relationship between model scale and downstream task performance for structured medical foundation models. Using a random sample (2.3 million patients, 32 hospitals) from a nationwide 519-hospital Japanese claims database, we pretrained encoder-only Transformers at five scales (2.2M-101M parameters) for disease incidence and medication prediction. Downstream performance saturated at task-dependent thresholds: disease prediction benefited from larger models (32M-101M), whereas medication prediction saturated at 11M, reducing pretraining time by 178 h. Across all tasks, the best-performing model consistently outperformed a Light Gradient Boosting Machine baseline in the area under the precision-recall curve. These findings indicate that, unlike the monotonically decreasing pretraining loss, the optimal model size varied depending on task characteristics. This task-dependent saturation provides practical guidance for balancing predictive performance and computational cost in structured medical foundation models.
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.