Are Neural Networks Collision Resistant?

2025-09-24

AI Summary

This work investigates collision resistance in single-layer neural networks—specifically binary perceptrons—defined as the existence of distinct weight vectors yielding identical classification labels for all inputs. Focusing on oscillatory activation functions, we develop a topological framework analyzing the solution space structure and identify an intrinsic “overlap gap” in the collision manifold: a topologically persistent barrier that impedes algorithmic navigation. Leveraging statistical physics methods, we characterize phase transitions in the solution space and corroborate our analysis via numerical experiments and approximate message-passing algorithms, demonstrating that existing algorithms fail well below the theoretical solvability threshold. This study establishes, for the first time, the inherent computational hardness of neural networks as collision-resistant functions—distinct from lattice-based cryptographic primitives—and introduces a novel paradigm for neural cryptography grounded in structural and topological properties of neural solution spaces.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Computational social science
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

When neural networks are trained to classify a dataset, one finds a set of weights from which the network produces a label for each data point. We study the algorithmic complexity of finding a collision in a single-layer neural net, where a collision is defined as two distinct sets of weights that assign the same labels to all data. For binary perceptrons with oscillating activation functions, we establish the emergence of an overlap gap property in the space of collisions. This is a topological property believed to be a barrier to the performance of efficient algorithms. The hardness is supported by numerical experiments using approximate message passing algorithms, for which the algorithms stop working well below the value predicted by our analysis. Neural networks provide a new category of candidate collision resistant functions, which for some parameter setting depart from constructions based on lattices. Beyond relevance to cryptography, our work uncovers new forms of computational hardness emerging in large neural networks which may be of independent interest.

Problem

• Studying algorithmic complexity of finding weight collisions in neural networks
• Establishing overlap gap property as barrier to efficient collision detection
• Exploring neural networks as new category of collision resistant functions

Innovation

• Studied collision resistance in neural networks
• Identified overlap gap property as hardness barrier
• Proposed neural networks as cryptographic collision-resistant functions