Lemmy: Bestiverse
  • Communities
  • Create Post
  • Create Community
  • heart
    Support Lemmy
  • search
    Search
  • Login
  • Sign Up
RSS BotMB to Hacker NewsEnglish · 3 hours ago

Machine Learnability as a Measure of Order in Aperiodic Sequences

arxiv.org

external-link
message-square
1
fedilink
5
external-link

Machine Learnability as a Measure of Order in Aperiodic Sequences

arxiv.org

RSS BotMB to Hacker NewsEnglish · 3 hours ago
message-square
1
fedilink
Research on the distribution of prime numbers has revealed a dual character: deterministic in definition yet exhibiting statistical behavior reminiscent of random processes. In this paper we show that it is possible to use an image-focused machine learning model to measure the comparative regularity of prime number fields at specific regions of an Ulam spiral. Specifically, we demonstrate that in pure accuracy terms, models trained on blocks extracted from regions of the spiral in the vicinity of 500m outperform models trained on blocks extracted from the region representing integers lower than 25m. This implies existence of more easily learnable order in the former region than in the latter. Moreover, a detailed breakdown of precision and recall scores seem to imply that the model is favouring a different approach to classification in different regions of the spiral, focusing more on identifying prime patterns at lower numbers and more on eliminating composites at higher numbers. This aligns with number theory conjectures suggesting that at higher orders of magnitude we should see diminishing noise in prime number distributions, with averages (density, AP equidistribution) coming to dominate, while local randomness regularises after scaling by log x. Taken together, these findings point toward an interesting possibility: that machine learning can serve as a new experimental instrument for number theory. Notably, the method shows potential 1 for investigating the patterns in strong and weak primes for cryptographic purposes.

Comments

alert-triangle
You must log in or register to comment.
  • PattyMcB@lemmy.world
    link
    fedilink
    English
    arrow-up
    1
    ·
    1 hour ago

    Seems plausible.

Hacker News

hackernews

Subscribe from Remote Instance

You are not logged in. However you can subscribe from another Fediverse account, for example Lemmy or Mastodon. To do this, paste the following into the search field of your instance: !hackernews@lemmy.bestiver.se
lock
Community locked: only moderators can create posts. You can still comment on posts.

Posts from the RSS Feed of HackerNews.

The feed sometimes contains ads and posts that have been removed by the mod team at HN.

Visibility: Public
globe

This community can be federated to other instances and be posted/commented in by their users.

  • 417 users / day
  • 1.55K users / week
  • 3.63K users / month
  • 9.61K users / 6 months
  • 2 local subscribers
  • 2.73K subscribers
  • 32.8K Posts
  • 13.8K Comments
  • Modlog
  • mods:
  • patrick
  • RSS Bot
  • BE: 0.19.5
  • Modlog
  • Instances
  • Docs
  • Code
  • join-lemmy.org