DeepMind paper: diffusion model factors 68-bit semiprimes, but compute costs scale exponentially
weballergy · x · 2026-11-10
A DeepMind team (Brendan O'Donoghue, Raia Hadsell, Demis Hassabis et al.) released a new preprint on semiprime factorization with machine learning.
- Method: transformers trained with discrete denoising diffusion, decoded via guided test-time beam search, learn to recover prime factors directly from data with no number-theoretic priors.
- Result: factored 68-bit integers, a substantial advance over the prior 56-bit ML state of the art.
- Division of labor: the diffusion model acts as a generative prior proposing candidate factors; exact verification or lattice-based post-processing completes the factorization.
- Scaling laws: unlike language, problem size drives scaling—fixed test accuracy requires compute that grows exponentially with bit length.
- Security implication: factoring cryptographically relevant integers remains computationally prohibitive, so no threat to current cryptography.
Related event: DeepMind Factors 68-Digit Semiprimes with Discrete Diffusion Models(3 posts)→
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