[HN Gopher] When models manipulate manifolds: The geometry of a ...
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       When models manipulate manifolds: The geometry of a counting task
        
       Author : vinhnx
       Score  : 88 points
       Date   : 2025-10-29 05:50 UTC (5 days ago)
        
 (HTM) web link (transformer-circuits.pub)
 (TXT) w3m dump (transformer-circuits.pub)
        
       | Rygian wrote:
       | > The task we study is linebreaking in fixed-width text.
       | 
       | I wonder why they focused specifically on a task that is already
       | solved algorithmically. The paper does not seem to address this,
       | and the references do not include any mentions of non-LLM
       | approaches to the line-breaking problem.
        
         | omnicognate wrote:
         | There's also a lot of analogising of this to visual/spatial
         | reasoning, even to the point of talking about "visual
         | illusions", when its clearly a counting task as the title says.
         | 
         | It makes it tedious to figure out what they actually did (which
         | sounds interesting) when it's couched in such terms and
         | presented in such an LLMified style.
        
           | dist-epoch wrote:
           | it's not strictly a counting task, the LLM sees same-sized-
           | tokens, but a token corresponds to a variable number of
           | characters (which is not directly fed into the model)
           | 
           | like the difference between Unicode code-points and UTF-8
           | bytes, you can't just count UTF-8 bytes to know how many
           | code-points you have
        
             | omnicognate wrote:
             | There's an aspect of figuring out what to count, but that
             | doesn't make this task visual/spatial in any sense I can
             | make out.
        
         | Legend2440 wrote:
         | They study it _because_ it already has a known solution.
         | 
         | The point is to see how LLMs implement algorithms internally,
         | starting with this simple easily understood algorithm.
        
           | Rygian wrote:
           | That makes sense; however it does not seem like they check
           | the LLM outputs against the known solution. Maybe I missed
           | that in the article.
        
           | catgary wrote:
           | I think this is an interesting direction, but I think that
           | step 2 of this would be to formulate some conjectures about
           | the geometry of other LLMs, or testable hypotheses about how
           | information flows wrt character counting. Even checking some
           | intermediate training weights of Haiku would be interesting,
           | so they'd still be working off of the same architecture.
           | 
           | The biology metaphor they make is interesting, because I
           | think a biologist would be the first to tell you that you
           | need more than one datapoint.
        
       | lccerina wrote:
       | Utter disrespect for using the term "biology" relating to LLM. No
       | one would call the analysis of a mechanical engine "car biology".
       | It's an artificial system, call it system analysis.
        
         | lewtun wrote:
         | The analogy stems from the notion that neural nets are "grown"
         | rather than "engineered". Chris Olah has an old, but good post
         | with some specific examples: https://colah.github.io/notes/bio-
         | analogies/
        
         | UltraSane wrote:
         | It makes sense if you define "biology" as "incredibly
         | complicated system not designed by humans that we kind of poke
         | at to try to understand it."
        
       | djoldman wrote:
       | A superior LLM for line length optimization:
       | 
       | https://www.youtube.com/watch?v=Y65FRxE7uMc
        
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