arXiv:2508.19445v3 Announce Type: replace Abstract: Given a trained neural network, can any specified output be generated by some input? Equivalently, does the network correspond to a function that is surjective? In generative models, surjectivity implies that any output, including harmful or undesirable content, can in principle be generated by the networks, raising concerns about model safety and jailbreak vulnerabilities. In this paper, we prove that many fundamental building blocks of modern neural architectures, such as networks with pre-layer normalization and linear-attention modules, a
This research provides theoretical grounding for critical safety and security concerns around advanced AI models, coinciding with increasing societal deployment and regulatory scrutiny of generative AI.
Understanding the surjectivity of neural networks highlights inherent vulnerabilities for generating harmful content, necessitating robust safety mechanisms and potentially rethinking architectural choices for AI models.
The theoretical proof suggests that a wide range of current AI architectures, by their fundamental design, can be forced to produce any arbitrary output, shifting the focus from 'if' to 'how' to mitigate this inherent capability.
- · AI safety researchers
- · Cybersecurity firms
- · Regulatory bodies
- · Generative AI developers (if they ignore safety)
- · Organizations deploying unchecked AI models
- · Users vulnerable to AI-generated harmful content
Increased focus and investment in provably safe AI architectures and robust alignment research.
Potential for new standards or regulatory requirements mandating proof of non-surjectivity or advanced guardrails for specific AI applications.
A shift in academic and industrial AI research towards designing models with inherent safety properties from the ground up, rather than relying solely on post-hoc filtering.
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Read at arXiv cs.LG