# A Vector Symbolic Approach to Multiple Instance Learning

arXiv: https://arxiv.org/abs/2511.16795 · HTML: https://mlsanity.com/paper/2511.16795/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 62 references that are in the map.
- First posted on arXiv 20 Nov 2025.

## Builds on (most cited first, 26 of 26)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Attention-based Deep Multiple Instance Learning](https://mlsanity.com/paper/1802.04712/) (2018)
- [TransMIL: Transformer based Correlated Multiple Instance Learning for Whole Slide Image Classification](https://mlsanity.com/paper/2106.00908/) (2021)
- [Dual-stream Multiple Instance Learning Network for Whole Slide Image Classification with Self-supervised Contrastive Learning](https://mlsanity.com/paper/2011.08939/) (2020)
- [A Metric Learning Reality Check](https://mlsanity.com/paper/2003.08505/) (2020)
- [ReZero is All You Need: Fast Convergence at Large Depth](https://mlsanity.com/paper/2003.04887/) (2020)
- [A Neuro-vector-symbolic Architecture for Solving Raven's Progressive Matrices](https://mlsanity.com/paper/2203.04571/) (2022)
- [Blessing of dimensionality: mathematical foundations of the statistical physics of data](https://mlsanity.com/paper/1801.03421/) (2018)
- [Multiple Instance Learning for Digital Pathology: A Review on the State-of-the-Art, Limitations & Future Potential](https://mlsanity.com/paper/2206.04425/) (2022)
- [Associative Long Short-Term Memory](https://mlsanity.com/paper/1602.03032/) (2016)
- [Vector Symbolic Architectures as a Computing Framework for Emerging Hardware](https://mlsanity.com/paper/2106.05268/) (2021)
- [GraphHD: Efficient graph classification using hyperdimensional computing](https://mlsanity.com/paper/2205.07826/) (2022)
- [Multiple instance learning with graph neural networks](https://mlsanity.com/paper/1906.04881/) (2019)
- [Learning with Holographic Reduced Representations](https://mlsanity.com/paper/2109.02157/) (2021)
- [Bringing UMAP Closer to the Speed of Light with GPU Acceleration](https://mlsanity.com/paper/2008.00325/) (2020)
- [xMIL: Insightful Explanations for Multiple Instance Learning in Histopathology](https://mlsanity.com/paper/2406.04280/) (2024)
- [Learning to Rank Question Answer Pairs with Holographic Dual LSTM Architecture](https://mlsanity.com/paper/1707.06372/) (2017)
- [Recasting Self-Attention with Holographic Reduced Representations](https://mlsanity.com/paper/2305.19534/) (2023)
- [HyperEmbed: Tradeoffs Between Resources and Performance in NLP Tasks with Hyperdimensional Computing enabled Embedding of n-gram Statistics](https://mlsanity.com/paper/2003.01821/) (2020)
- [Reproducibility in Multiple Instance Learning: A Case For Algorithmic Unit Tests](https://mlsanity.com/paper/2310.17867/) (2023)
- [Deploying Convolutional Networks on Untrusted Platforms Using 2D Holographic Reduced Representations](https://mlsanity.com/paper/2206.05893/) (2022)
- [Holographic Global Convolutional Networks for Long-Range Prediction Tasks in Malware Detection](https://mlsanity.com/paper/2403.17978/) (2024)
- [Towards Generalization in Subitizing with Neuro-Symbolic Loss using Holographic Reduced Representations](https://mlsanity.com/paper/2312.15310/) (2023)
- [A Walsh Hadamard Derived Linear Vector Symbolic Architecture](https://mlsanity.com/paper/2410.22669/) (2024)
- [Assembling Modular, Hierarchical Cognitive Map Learners with Hyperdimensional Computing](https://mlsanity.com/paper/2404.19051/) (2024)
- [Linearithmic Clean-up for Vector-Symbolic Key-Value Memory with Kroneker Rotation Products](https://mlsanity.com/paper/2506.15793/) (2025)

## Abstract (arXiv)

Multiple Instance Learning (MIL) tasks impose a strict logical constraint: a bag is labeled positive if and only if at least one instance within it is positive. While this iff constraint aligns with many real-world applications, recent work has shown that most deep learning-based MIL approaches violate it, leading to inflated performance metrics and poor generalization. We propose a novel MIL framework based on Vector Symbolic Architectures (VSAs), which provide a differentiable mechanism for performing symbolic operations in high-dimensional space. Our method encodes the MIL assumption directly into the model's structure by representing instances and concepts as nearly orthogonal high-dimensional vectors and using algebraic operations to enforce the iff constraint during classification. To bridge the gap between raw data and VSA representations, we design a learned encoder that transforms input instances into VSA-compatible vectors while preserving key distributional properties. Our approach, which includes a VSA-driven MaxNetwork classifier, achieves state-of-the-art results for a valid MIL model on standard MIL benchmarks and medical imaging datasets, outperforming existing methods while maintaining strict adherence to the MIL formulation. This work offers a principled, interpretable, and effective alternative to existing MIL approaches that rely on learned heuristics.