# BiSHop: Bi-Directional Cellular Learning for Tabular Data with Generalized Sparse Modern Hopfield Model

arXiv: https://arxiv.org/abs/2404.03830 · HTML: https://mlsanity.com/paper/2404.03830/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 89 references that are in the map.
- First posted on arXiv 4 Apr 2024.

## Builds on (most cited first, 30 of 54)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [Efficient Transformers: A Survey](https://mlsanity.com/paper/2009.06732/) (2020)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [TabNet: Attentive Interpretable Tabular Learning](https://mlsanity.com/paper/1908.07442/) (2019)
- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [TabTransformer: Tabular Data Modeling Using Contextual Embeddings](https://mlsanity.com/paper/2012.06678/) (2020)
- [SAINT: Improved Neural Networks for Tabular Data via Row Attention and Contrastive Pre-Training](https://mlsanity.com/paper/2106.01342/) (2021)
- [Dense Associative Memory for Pattern Recognition](https://mlsanity.com/paper/1606.01164/) (2016)
- [When Do Neural Nets Outperform Boosted Trees on Tabular Data?](https://mlsanity.com/paper/2305.02997/) (2023)
- [Neural Oblivious Decision Ensembles for Deep Learning on Tabular Data](https://mlsanity.com/paper/1909.06312/) (2019)
- [On Embeddings for Numerical Features in Tabular Deep Learning](https://mlsanity.com/paper/2203.05556/) (2022)
- [Sparse Sequence-to-Sequence Models](https://mlsanity.com/paper/1905.05702/) (2019)
- [Birth of a Transformer: A Memory Viewpoint](https://mlsanity.com/paper/2306.00802/) (2023)
- [Blockwise Self-Attention for Long Document Understanding](https://mlsanity.com/paper/1911.02972/) (2019)
- [Adaptively Sparse Transformers](https://mlsanity.com/paper/1909.00015/) (2019)
- [Well-tuned Simple Nets Excel on Tabular Datasets](https://mlsanity.com/paper/2106.11189/) (2021)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [DNABERT-2: Efficient Foundation Model and Benchmark For Multi-Species Genome](https://mlsanity.com/paper/2306.15006/) (2023)
- [Large Associative Memory Problem in Neurobiology and Machine Learning](https://mlsanity.com/paper/2008.06996/) (2020)

## Built on by (most cited first, 21 of 21)

- [TALENT: A Tabular Analytics and Learning Toolbox](https://mlsanity.com/paper/2407.04057/) (2024)
- [Representation Learning for Tabular Data: A Comprehensive Survey](https://mlsanity.com/paper/2504.16109/) (2025)
- [Computational Limits of Low-Rank Adaptation (LoRA) Fine-Tuning for Transformer Models](https://mlsanity.com/paper/2406.03136/) (2024)
- [PTaRL: Prototype-based Tabular Representation Learning via Space Calibration](https://mlsanity.com/paper/2407.05364/) (2024)
- [Multi-Layer Transformers Gradient Can be Approximated in Almost Linear Time](https://mlsanity.com/paper/2408.13233/) (2024)
- [Bypassing the Exponential Dependency: Looped Transformers Efficiently Learn In-context by Multi-step Gradient Descent](https://mlsanity.com/paper/2410.11268/) (2024)
- [The Computational Limits of State-Space Models and Mamba via the Lens of Circuit Complexity](https://mlsanity.com/paper/2412.06148/) (2024)
- [Conv-CoA: Improving Open-domain Question Answering in Large Language Models via Conversational Chain-of-Action](https://mlsanity.com/paper/2405.17822/) (2024)
- [HSR-Enhanced Sparse Attention Acceleration](https://mlsanity.com/paper/2410.10165/) (2024)
- [Provably Optimal Memory Capacity for Modern Hopfield Models: Transformer-Compatible Dense Associative Memories as Spherical Codes](https://mlsanity.com/paper/2410.23126/) (2024)
- [A Survey on Deep Tabular Learning](https://mlsanity.com/paper/2410.12034/) (2024)
- [Nonparametric Modern Hopfield Models](https://mlsanity.com/paper/2404.03900/) (2024)
- [Provable Differentially Private Computation of the Cross-Attention Mechanism](https://mlsanity.com/paper/2407.14717/) (2024)
- [Theoretical Constraints on the Expressive Power of mathsfRoPE-based Tensor Attention Transformers](https://mlsanity.com/paper/2412.18040/) (2024)
- [Modern Hopfield Networks Require Chain-of-Thought to Solve mathsfNC1-Hard Problems](https://mlsanity.com/paper/2412.05562/) (2024)
- [Fast and Low-Cost Genomic Foundation Models via Outlier Removal](https://mlsanity.com/paper/2505.00598/) (2025)
- [Unlocking the Theory Behind Scaling 1-Bit Neural Networks](https://mlsanity.com/paper/2411.01663/) (2024)
- [Neural Algorithmic Reasoning for Hypergraphs with Looped Transformers](https://mlsanity.com/paper/2501.10688/) (2025)
- [Time and Memory Trade-off of KV-Cache Compression in Tensor Transformer Decoding](https://mlsanity.com/paper/2503.11108/) (2025)
- [Multi-branch of Attention Yields Accurate Results for Tabular Data](https://mlsanity.com/paper/2502.12507/) (2025)
- [TabNSM: Neural Sparse Mixer for Tabular Regression](https://mlsanity.com/paper/2608.18026/) (2026)

## Abstract (arXiv)

We introduce the Bi-Directional Sparse Hopfield Network (BiSHop), a novel end-to-end framework for deep tabular learning. BiSHop handles the two major challenges of deep tabular learning: non-rotationally invariant data structure and feature sparsity in tabular data. Our key motivation comes from the recent established connection between associative memory and attention mechanisms. Consequently, BiSHop uses a dual-component approach, sequentially processing data both column-wise and row-wise through two interconnected directional learning modules. Computationally, these modules house layers of generalized sparse modern Hopfield layers, a sparse extension of the modern Hopfield model with adaptable sparsity. Methodologically, BiSHop facilitates multi-scale representation learning, capturing both intra-feature and inter-feature interactions, with adaptive sparsity at each scale. Empirically, through experiments on diverse real-world datasets, we demonstrate that BiSHop surpasses current SOTA methods with significantly less HPO runs, marking it a robust solution for deep tabular learning.