# LoopICL: Looping a single transformer block to solve tabular tasks

arXiv: https://arxiv.org/abs/2609.36108 · HTML: https://mlsanity.com/paper/2609.36108/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 50 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 30 of 41)

- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [CogView: Mastering Text-to-Image Generation via Transformers](https://mlsanity.com/paper/2105.13290/) (2021)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021)
- [TabICL: A Tabular Foundation Model for In-Context Learning on Large Data](https://mlsanity.com/paper/2502.05564/) (2025)
- [ReZero is All You Need: Fast Convergence at Large Depth](https://mlsanity.com/paper/2003.04887/) (2020)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [When Do Neural Nets Outperform Boosted Trees on Tabular Data?](https://mlsanity.com/paper/2305.02997/) (2023)
- [TabArena: A Living Benchmark for Machine Learning on Tabular Data](https://mlsanity.com/paper/2506.16791/) (2025)
- [Looped Transformers are Better at Learning Learning Algorithms](https://mlsanity.com/paper/2311.12424/) (2023)
- [TabICLv2: A better, faster, scalable, and open tabular foundation model](https://mlsanity.com/paper/2602.11139/) (2026)
- [Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks](https://mlsanity.com/paper/2106.04537/) (2021)
- [Self-Attention Between Datapoints: Going Beyond Individual Input-Output Pairs in Deep Learning](https://mlsanity.com/paper/2106.02584/) (2021)
- [Looped Transformers for Length Generalization](https://mlsanity.com/paper/2409.15647/) (2024)
- [On Training Implicit Models](https://mlsanity.com/paper/2111.05177/) (2021)
- [LoopFormer: Elastic-Depth Looped Transformers for Latent Reasoning via Shortcut Modulation](https://mlsanity.com/paper/2602.11451/) (2026)
- [TALENT: A Tabular Analytics and Learning Toolbox](https://mlsanity.com/paper/2407.04057/) (2024)
- [A Mechanistic Analysis of Looped Reasoning Language Models](https://mlsanity.com/paper/2604.11791/) (2026)
- [Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers](https://mlsanity.com/paper/2606.18206/) (2026)
- [Mambular: A Sequential Model for Tabular Deep Learning](https://mlsanity.com/paper/2408.06291/) (2024)
- [Stabilizing Recurrent Dynamics for Test-Time Scalable Latent Reasoning in Looped Language Models](https://mlsanity.com/paper/2605.26733/) (2026)
- [ELT: Elastic Looped Transformers for Visual Generation](https://mlsanity.com/paper/2604.09168/) (2026)
- [Memory-Efficient Looped Transformer: Decoupling Compute from Memory in Looped Language Models](https://mlsanity.com/paper/2605.07721/) (2026)
- [Early Stopping Tabular In-Context Learning](https://mlsanity.com/paper/2506.21387/) (2025)
- [Is One Layer Enough? Understanding Inference Dynamics in Tabular Foundation Models](https://mlsanity.com/paper/2605.06510/) (2026)
- [On the Residual Scaling of Looped Transformers: Stability and Transferability](https://mlsanity.com/paper/2606.18524/) (2026)

## Abstract (arXiv)

Tabular foundation models using in-context learning have recently surpassed gradient-boosted trees on predictive tabular tasks. However, recent mechanistic insights suggest that parameters in these models are largely redundant. We introduce LoopICL, a looped transformer whose core design decouples parameter count from computational depth. LoopICL consists of a single block, processing data through two coupled streams: a cell stream capturing per-cell feature representations and a row stream capturing in-context example representations, jointly refined through within-column and cross-column attention. During pre-training, we vary loop counts, allowing the block to be unrolled for a varying number of iterations at test-time and use a learned exit-gate to automatically exit. In its standard setting, LoopICL performs competitively with TabICLv2 on TabArena and TALENT at the same computational cost (FLOPs), while using nearly 90% fewer parameters. Furthermore, its recurrent design enables users to also trade off inference cost and performance, providing a resource-aware TFM.