A Vector Symbolic Approach to Multiple Instance Learning

TL;DR

This paper introduces a novel Vector Symbolic Architecture-based framework for Multiple Instance Learning that enforces the logical constraints of MIL, achieving state-of-the-art results while maintaining interpretability.

Contribution

It presents a VSA-based MIL model with a learned encoder and MaxNetwork classifier that strictly enforces MIL constraints and outperforms existing methods.

Findings

Achieves state-of-the-art results on standard MIL benchmarks.

Maintains strict adherence to MIL logical constraints.

Provides an interpretable, principled approach to MIL.

Abstract

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.