A Vector Symbolic Approach to Multiple Instance Learning

2025-11-20

AI Summary

Multi-instance learning (MIL) imposes a strict logical constraint: a bag is labeled positive *if and only if* it contains at least one positive instance. However, mainstream deep learning approaches violate this constraint, leading to inflated evaluation metrics and degraded generalization. To address this, we propose the first differentiable Vector Symbolic Architecture (VSA) framework explicitly embedding MIL’s formal logic: instances are mapped to high-dimensional symbolic vectors, and VSA algebraic operations—particularly binding and unbinding—are leveraged to explicitly encode existential quantification (“there exists”). We further introduce a learnable VSA-MaxNetwork classifier enabling end-to-end differentiable inference. Our approach uniquely unifies differentiable symbolic reasoning with deep learning, intrinsically enforcing the MIL assumption at the architectural level—thereby enhancing both interpretability and generalization. Extensive experiments on standard MIL benchmarks and medical imaging datasets demonstrate state-of-the-art performance while strictly adhering to the formal MIL definition.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Computer Vision: Visual Reasoning & Symbolic Representations
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Enforcing logical iff constraint in Multiple Instance Learning classification
• Bridging raw data with symbolic representations using learned encoders
• Providing interpretable MIL framework with strict constraint adherence

Innovation

• Vector Symbolic Architectures encode MIL constraints
• Learned encoder bridges data to VSA representations
• VSA-driven MaxNetwork classifier ensures strict MIL adherence