[HN Gopher] Pareto Front
       ___________________________________________________________________
        
       Pareto Front
        
       Author : binyu
       Score  : 247 points
       Date   : 2026-07-29 12:12 UTC (8 days ago)
        
 (HTM) web link (en.wikipedia.org)
 (TXT) w3m dump (en.wikipedia.org)
        
       | soupspaces wrote:
       | https://www.mayerowitz.io/blog/mario-meets-pareto
        
         | cubefox wrote:
         | https://news.ycombinator.com/item?id=49195231
        
       | Aachen wrote:
       | Misread the title and got excited about a Pareto font, that is,
       | the best possible font (presumably: distinct l/I, O/0, scores
       | within error margins of the top readability and reading speed
       | scores, widely available, etc.)
       | 
       | Maybe in vein but did anyone already figure this one out? The
       | closest I got was PT sans, open-licensed commissioned by the
       | Russian ministry for communication (I found it surprising that a
       | country that doesn't use Latin script made the best font!), but
       | it's not widely shipped so you need to figure out how to include
       | font files whenever you want to use it
        
         | adornKey wrote:
         | I'd also be interested in the Pareto Front of Fonts. That would
         | be the final font collection - to rule them all.
        
         | joshka wrote:
         | lol same :D
        
         | airstrike wrote:
         | Inter with optional open type features turned on?
         | 
         | https://rsms.me/inter/
        
           | Aachen wrote:
           | I didn't know fonts can have options. Another learning curve
           | on how to enable that in Latex/Html/Libreoffice/anywhere else
           | I use fonts ^^'. But still helpful to know about!
           | 
           | ss02 disambiguation seems to be the one I'd be wanting to
           | turn on, with tnum for monospace numbers being a good option
           | as well that I hadn't even realised I wanted from a font!
        
             | airstrike wrote:
             | Yeah, those features are awesome! Sadly support for them is
             | quite lacking in applications...
             | 
             | Tabular numbers are awesome!
        
               | notpushkin wrote:
               | I feel like there should be a GUI tool to bake in any
               | alternates into the font itself.
        
               | airstrike wrote:
               | Ok, I'll make it!
        
               | cheesecakegood wrote:
               | You mean like Commit Mono does? https://commitmono.com/
        
         | gadders wrote:
         | I thought it was some sort of Italian activism group.
         | 
         | "The Pareto Front today claimed responsiblity for...."
        
           | orthoxerox wrote:
           | ...20% of the attacks causing 80% of the casualties?
        
             | mdnahas wrote:
             | As someone with an Italian grandmother and both a CS and
             | Econ degree, I got a great laugh out of this joke! Bravo!
        
             | pphysch wrote:
             | No!! That is the Front of Pareto[1], a totally different
             | group. Our Pareto Front only causes 20% of the casualties.
             | 
             | [1] -
             | http://montypython.50webs.com/scripts/Life_of_Brian/8.htm
        
           | lucaslazarus wrote:
           | You mean the People's front of Pareto!
        
             | croisillon wrote:
             | splitters!
        
         | __s wrote:
         | Trouble with fonts is sometimes monospace good, sometimes
         | monodpace bad
         | 
         | Anyways I'll namedrop Iosevka as perfect monospace font for
         | working on 13" laptop
        
           | throw-the-towel wrote:
           | Seconding Iosevka, it's great for code! And you can get a
           | version without ligatures.
        
             | Aachen wrote:
             | That looks... swingy! Took a second to get used to it but I
             | think I like the refreshing take for a monospace font :)
             | https://fonts.google.com/specimen/Iosevka+Charon+Mono
        
         | arduanika wrote:
         | No, it's far from the best possible font, but to its credit, it
         | gets most aspects of typography right by just focusing on the
         | ~1/5 of the requirements that actually really count.
        
           | Aachen wrote:
           | What are the 4/5ths that you don't like, and which one(s)
           | would you recommend instead? (I'm mostly interested/focussed
           | on the sans variant but also happy to hear about serif and
           | mono)
        
             | arduanika wrote:
             | It's not that I don't _like_ them. It 's more just that
             | some of these design considerations are not worth the
             | effort to fret over, and if you're smart about your time,
             | doing 1/5 of the work will get you something like ~4/5 of
             | the results.
        
               | notpushkin wrote:
               | ...so it _is_ the Pareto font indeed!
        
         | peesem wrote:
         | look at Atkinson Hyperlegible? commissioned by the Braille
         | foundation for low-vision readers which means it's very
         | readable
        
           | Aachen wrote:
           | Huh, I'm positive this was one of the first I considered (or
           | perhaps it was a different dyslexia font) but I can't find
           | the reason why I would have preferred PT Sans over this. Each
           | has some pros and cons: PT Sans has same-width digits;
           | Hyperlegible has a nicer-looking Q (imo); PT Sans has a
           | normal-looking zero (not struck); Hyperlegible has a normal-
           | looking 'fi' combination (no ligature that merges the two
           | characters into a new one); Hyperlegible has a 6 distinct
           | from an inverted 9; PT Sans needs a bit less horizontal
           | space. The font specifically designed for accessibility
           | should be the easy winner if all else is equal anyway
           | 
           | They apparently released Hyperlegible Next in 2025 which,
           | flipping between tabs on Google Fonts (since the original
           | website doesn't show the fonts), is nearly identical but has
           | five new weight settings (nobody should imo ever use thin
           | fonts though, it noticeably harms readability for me and my
           | sight is only the tiniest bit below normal vision, but ok
           | it's an option) and improved kerning (the original font had
           | extremely little space between 'll', for example)
           | 
           | The 2025 version sadly doesn't ship with my version of
           | TexLive, but the original (from 2020) already does so that
           | makes it easy to use as well! Cool stuff, thanks for the tip
           | :)
        
       | bhanu786 wrote:
       | may, anyone explain what is this
        
         | ChrisMarshallNY wrote:
         | Basically, prioritization.
         | 
         | It's really that simple.
         | 
         | Eschew obfuscation.
        
           | bhanu786 wrote:
           | you have confused me
        
           | Lerc wrote:
           | Almost the complete opposite of prioritisation.
           | 
           | The Pareto points are where you sacrifice the least of
           | anything to get the most of everything.
           | 
           | There's the saying about buying computers. Good, Cheap, Fast,
           | pick any two. That's where you would prioritise.
           | 
           | If someone makes something that better, cheaper, and faster,
           | or even pretty close to the best on two of those and clearly
           | better on the other. It's a Pareto point.
           | 
           | Over time computers are getting better, cheaper and faster
           | (software notwithstanding). The leading edge of that advance
           | of all of the things is the Pareto front.
        
             | jrrv wrote:
             | Given this in the TFA
             | 
             | > a Pareto front represents the set of solutions where no
             | solution outperforms any other solution in the set at every
             | objective
             | 
             | I do not believe you are correct when you say
             | 
             | > something that better, cheaper, and faster, or even
             | pretty close to the best on two of those and clearly better
             | on the other. It's a Pareto point.
             | 
             | Since that would outperform on every objective
             | 
             | GP's point that it's prioritisation does not seem incorrect
             | to me. Prioritisation involves considering trade-offs of
             | various approaches and deciding which aspects & attributes
             | to optimise for, at the expense of others.
        
             | ChrisMarshallNY wrote:
             | I'm not sure how that's the opposite of prioritizing, but
             | if I'm wrong, then I'll happily admit it.
             | 
             | We choose our items/workflows/technologies/whatever, so we
             | get the best/most efficient/most effective/whatever, across
             | the widest possible set.
             | 
             | Sounds like prioritizing, to me, but I'm just a dumb hick,
             | so I suppose I can be wrong.
        
               | Lerc wrote:
               | Prioritising is when you choose something over another. A
               | drag racer prioritises time to travel a quarter mile.
               | 
               | Going for the Pareto is when you elect not to prioritise.
               | It is explicitly deciding to not choose one property over
               | another ant to keep everything as much as you can.
        
               | ChrisMarshallNY wrote:
               | I read it as finding the point of maximum effectiveness.
               | The point at which the most is done for the most.
               | 
               | Getting to that point can be calculated (in some cases),
               | but I suspect most folks get there by trial and error.
               | Finding out what is effective, and what is not, and
               | choosing what is effective, over what is not, until
               | there's no longer a choice. That often becomes tribal
               | knowledge, and is handed down. There's always someone
               | trying to improve it, and when they figure it out, that
               | gets added to the tribal knowledge. Basically, that's how
               | nature does it, so there's some serious prior art.
               | Natural Selection is _brutal_ prioritization.
               | 
               | In Morocco, they used to announce the end of the Ramadan
               | fast, by holding up a black thread and a white thread,
               | and waiting until they could not tell the difference.
               | 
               | Then, they'd fire a cannon, and everybody would dig into
               | some awesome soup. Sort of the same thing.
        
           | stevefan1999 wrote:
           | No, it's more about maximizing the utility function and
           | finding the "shield" where you'd start getting diminishing
           | return beyond that
        
         | isoprophlex wrote:
         | "what's the family of optimal choices when you have multiple
         | dimensions to rank on?"
         | 
         | Say a race vehicle has acceleration, top speed as defining
         | parameters. Some are slow but accelerate hard, others need a
         | long time to reach very high top speeds. Others are in between,
         | or just flat out bad at both.
         | 
         | The pareto frontier is the set of vehicles that are best: pick
         | one from the frontier and you can be sure that for it's given
         | top speed, none accelerate faster. And vice versa, pick one
         | with a given acceletation and you are sure none have a better
         | top speed
        
         | continuational wrote:
         | When you have a tradeoff between two parameters, which points
         | dominate the others in the sense that you can't choose another
         | point without getting less of one of the parameters.
        
           | bhanu786 wrote:
           | thanks, may you tell me where we can use them?
        
             | joshka wrote:
             | The current thing that comes up regularly is choosing an
             | LLM setup.
        
         | felixguendling wrote:
         | If you optimize one criterion, it's simple: lowest is best or
         | highest is best. If you optimize multiple criteria, all optimal
         | trade offs between any of the selected criteria are "best" in
         | some way.
        
         | chriswarbo wrote:
         | If we have a set of things (e.g. language models) and some
         | measures we care about (e.g. cost, speed, whether weights are
         | open, scores for a few benchmarks, etc.), then some of those
         | things will be "pareto optimal" (see below) and some won't. The
         | "pareto front" is the subset that is pareto optimal.
         | 
         | Some thing is "pareto optimal" when there isn't another thing
         | that's AT LEAST AS GOOD in ALL measures, and BETTER in at least
         | one way. For example, if we say there are no ties (for
         | simplicity), then the cheapest language model is pareto
         | optimal; the fastest model is pareto optimal; those which score
         | highest on each benchmark are pareto optimal; and so on.
         | 
         | Tradeoffs can also be pareto optimal: for example, if the
         | cheapest model is also slow, then there will be more pareto
         | optimal models which are "cheapest for their speed"; and so on
         | for other tradeoffs (e.g. fastest that achieves a certain
         | benchmark score; cheapest model with open weights; etc.).
         | 
         | If you're making a decision about which thing to choose, you
         | only need to care about those in the pareto front (since, by
         | definition, anything that's not pareto optimal is objectively
         | worse on at least one measure).
         | 
         | Pareto optimality does not compare one measure against another:
         | something that's 10000x slower can still be pareto optimal, if
         | it's 1% cheaper than the alternatives. To pick a "best" thing,
         | you could give a weight/importance to each measure, and combine
         | them into an overall score: but that's subjective, and might
         | vary between people and tasks. In contrast, focusing on the
         | pareto front is a way to ignore those things that will never be
         | the best, regardless of weighting.
        
           | matsemann wrote:
           | I honestly think the wikipedia article is too complicated. My
           | own image example here as an another attempt to explain:
           | https://imgur.com/a/5ZQIJDb
           | 
           | Mapping the cost of something (like an algorithm), and the
           | time it takes (so lower is better for both). 1, 3 and 5 are
           | all optimal in their own sense. No one is strictly better
           | than the other, just different tradeoffs you have to choose
           | yourself. However, you would never choose 2, because for a
           | lower cost you could get the same result choosing 3. Same
           | with 4, 6 and 7, they all have something that's both faster
           | and at the same time just as cheap you could choose.
           | 
           | A pareto front is a bit like the classical "fast, cheap,
           | good, choose 2". There are always tradeoffs, but if something
           | is both slow, expensive and not better than something that's
           | faster and cheaper, it's a bad choice, and thus not on the
           | "pareto front".
        
       | denismenace wrote:
       | I'm assuming you must have discovered this through the OpenRouter
       | LLM performance graphs.
        
         | miyuru wrote:
         | artificialanalysis for me.
         | 
         | https://artificialanalysis.ai/#intelligence-comparison-tabs
        
           | trash_cat wrote:
           | I think the one from hugging face is much clearer, albeit its
           | an arena metric and a bit tricky to find the pareto view.
           | Look for the the top Navigation Bar (Agent Chat Code Image
           | Video). Chat -> (dropdown) Text -> (Side panel) View as
           | Pareto.
           | 
           | https://huggingface.co/spaces/lmarena-ai/arena-leaderboard
        
         | Aachen wrote:
         | First mention in chats for me was September 2016. Not sure how
         | that topic came up but LLMs aren't the only way to get there.
         | It's also a rather obvious principle to come up with, at least
         | I'm pretty sure I was doing it without thinking I should name
         | the concept of picking the option that best fits your
         | requirements
        
       | gpt5 wrote:
       | You can see the Pareto Frontier well in DeepSWE's chart here -
       | https://deepswe.datacurve.ai/
       | 
       | ChatGPT 5.6 Luna on the right (cheaper) cover most of the
       | frontier, with a point for Deepseek flash, and higher performance
       | overlapping heavily between 5.6 Sol and Fable.
       | 
       | That DeepSeek point will probably move back towards Luna as
       | deepseek announced a "significant" price increase coming to their
       | API [1], which kind of demonstrates that beating the Pareto
       | frontier is where the difficulty actually is).
       | 
       | [1]
       | https://www.bloomberg.com/news/articles/2026-08-06/deepseek-...
        
         | kooi wrote:
         | I've been wondering if OpenAI make Luna artificially cheap to
         | get people into their eco system.
         | 
         | I think it's great and hope the price can stay the same.
        
           | bob1029 wrote:
           | I think Luna might be just small enough to provide some kind
           | of stepwise improvement in how it is hosted.
           | 
           | Going from 81GB of weights to 79GB of weights can mean a 50%
           | reduction in GPU capacity required.
           | 
           | If you can fit a model in just one GPU (or rack) as opposed
           | to across an entire datacenter, the latency gains can be
           | substantial too. If you can reduce token latency by half,
           | that would double the amount of customers you could support.
        
       | CodeIsTheEnd wrote:
       | I am training for a marathon, and, as I increase both by distance
       | and pace, I am always excited when I have a "Pareto run": a run
       | along the Pareto frontier of me trying to maximize distance and
       | speed.
       | 
       | When explaining it to some coworkers, I stumbled on a fairly
       | intuitive explanation: "I've run farther before, and I've run
       | faster before, but I've never run _this_ far, _this fast."
       | 
       | There was some pushback about why not just call it a PR (personal
       | record), but I would only use that term for fixed distances (1mi,
       | 5k, 10k, etc.) or a consistent route that I've run many times
       | before. Nobody would say "I set my 7.40 mile PR today." More
       | importantly, it misses the comparison to all farther (and faster)
       | runs--it's not exciting to set a 5k PR just because you've barely
       | run that distance before, and the pace is actually slower that a
       | 10k you've done.
       | 
       | (Had a Pareto run of 7.40 miles @ 6:28/mi last week!)
        
         | froxtrot wrote:
         | Not relevant to pareto, but that's a really fun way to look at
         | running. Not quite as fast as your pareto run shows, but I'll
         | definitely keep that metric back of mind to keep the psyche
         | high for running.
        
         | reedf1 wrote:
         | The cycling equivalent is your power curve, i.e. the longest
         | you've held a power for a certain time interval.
        
         | voidhorse wrote:
         | So, while it's true that your runs with high speed _and_
         | distance when both are considered are Pareto points, your max
         | speed run and max distance run overall are _also_ Pareto
         | points. So calling these high distance+speed runs  "Pareto"
         | doesn't actually distinguish them completely from other runs.
         | 
         | A point is Pareto so long as it is _non-dominated_ --that is,
         | you're not looking for dominating points, you're looking for
         | points that are "no worse" than all others, in all criteria,
         | _when you consider that point as a reference_.
         | 
         | So your Pareto Runs are indeed Pareto points. However, your run
         | with your fastest possible speed, even if your distance was
         | really bad, is also still a Pareto efficient point.
         | 
         | (Taking >= as more efficient here) By definition, the point A
         | is Pareto if there is no point B such that in all criteria, B
         | >= A, and for at least one criteria B > A. Take the run with
         | the best speed. It is Pareto because we cannot find a single
         | point B that satisfies both of these conditions. Your "Pareto
         | Run" doesn't satisfy this set of conditions because it is worse
         | in terms of speed, even if it has better distance than the max
         | speed point.
         | 
         | The only way your Pareto runs would be the only Pareto points
         | in your record is if they simultaneously hit maxima for
         | distance and speed when compared _to all other points_. So, for
         | them to be the sole Pareto point, the clause  ""I've run
         | farther before, and I've run faster before..." would have to be
         | false! The point would have to break both your all time records
         | to be the solitary Pareto point. With running, because of how
         | speed and distance are related this will basically never
         | happen.
         | 
         | The definition of Pareto efficiency is essentially _negative in
         | nature_ --it's not about finding specific dominating points,
         | it's about finding points that are _not dominated by any
         | others_ on any criterion, period. All criteria are weighted
         | equally in the search for Pareto points. It doesn 't build in
         | any weighting like considering maximum across criteria as
         | "better" than points that only maximize one criteria. For a
         | "biobjective" problem like your runs, the Pareto set will
         | always contain the points (MAX, -) and (-, MAX)--they may not
         | be unique over the criteria but there will always be at least
         | one representative for each, I believe.
        
           | speedstyle wrote:
           | They never said it was the only Pareto run? Just a _new_ one,
           | improving the overall Pareto front
        
       | vavikk wrote:
       | Nice, this is exactly what I use for the multi-objective
       | optimizer on a quantum network simulator I'm building -- scoring
       | topologies on fidelity/latency/success rate tradeoffs.
        
         | matsemann wrote:
         | My thesis many years ago was on multi-objective optimization
         | using evolutionary algorithms (in my profile), and maintaining
         | a wide pareto front was what most algorithms (like NSGA-II)
         | were attempting. If all individuals cluster around a small area
         | (in for instance a weight/strength tradeoff), you will quickly
         | get stuck. So should select solutions to keep for further
         | search along the whole front (for instance some solution that
         | is very strong but unfortunately also very heavy). Maybe keep
         | some of them as candidates even if worse (not part of the
         | pareto front), just to keep that part of the search space alive
         | and avoid local optima.
         | 
         | Of course, what's hard anyways when you have a good set of
         | solutions that are pareto optimal, is to then choose between
         | them. Especially as the dimensions (objectives) grow. In my
         | example we can end up with many variants of strength/weight
         | trade-offs that each are optimal, which one to choose?
        
       | lorey wrote:
       | Found this to display the optimal LLM choice while building
       | evalry. It's such a useful tool, not only for thinking about it,
       | but for visualization, too.
       | 
       | Example: Which LLM gives me the best ELI5 explanations for a
       | given price. https://evalry.com/benchmarks/explain-like-i-m-5-321
        
       | bob1029 wrote:
       | Pareto front sounds like an interesting way to optimize, but it
       | suffers from the curse of dimensionality just like anything else.
       | 
       | As the number of objectives (dimensions) increases, the number of
       | samples you need to cover the frontier increases exponentially.
       | You will very rarely find solutions that actually dominate other
       | solutions in many practical optimization scenarios. With 2
       | dimensions you have a 25% chance of domination. With 10
       | dimensions it's a .098% chance.
       | 
       | The most useful cases I've seen tend to occur where we just
       | optimize for two things at once. The chances of domination are
       | high, it's easy to visualize and very efficient to implement. As
       | we get into higher dimensional spaces, things get weird really
       | fast.
        
         | krapht wrote:
         | One I spent a few months working on was pathfinding for trucks.
         | The goal is to find dominant solutions over {shortest time,
         | lowest cost (tolls + fuel), avg road speed variance - traffic
         | sensitivity} and then return 3-4 routes that are equal distance
         | from each other in this dimensional space for users to pick
         | from.
         | 
         | As you say, the most useful things happen in low-dimensional
         | spaces.
        
         | peri-cl wrote:
         | > _" As we get into higher dimensional spaces, things get weird
         | really fast."_
         | 
         | The geometric problem of computing a _d_ -dimensional Pareto
         | set of cardinality _n_
         | 
         | https://en.wikipedia.org/wiki/Maxima_of_a_point_set
         | 
         | has a truly weird property not covered by the computational
         | complexity discussion on that page. It says there's an
         | algorithm achieving O(n log(n)^(d-3) log log n), which is true
         | and also a lie. The algorithm that achieves that asymptotic
         | form is a galactic algorithm; and not an ordinary one in the
         | sense of "has a large constant multiplicative factor", but one
         | with this property (I've never found any other algorithm which
         | exhibits it):
         | 
         |  _The runtime is within a bounded constant factor of n^2, for
         | all n up to some critical N whose size is exponential in d_ (I
         | think it was exactly 2^d or something).
         | 
         | I.e. the runtime has "two shapes": it's purely quadratic up to
         | a galactically-large constant, and thereafter has a transition
         | into to a slower function. The asymptotic version in the
         | textbooks isn't achievable in the real world (for all but very
         | small dimension).
         | 
         | There's an elementary proof using generating functions.
         | 
         | edit to add: If anyone's curious about it, a simplified version
         | of the recurrence relation that's enough to exhibit this
         | behavior (you can instantly see it if you graph this
         | numerically) is                   f(n,d=0) = 1         f(n=1,d)
         | = 1         f(n,d)   = n + 2f([?]n/2[?], d) + 2f([?]n/2[?],
         | d-1)
        
         | jonathaneunice wrote:
         | The curse of dimensionality times the reality that good metrics
         | are elusive or themselves a bit cursed. Many outcomes you're
         | engineering or product-managing toward are quite squishy, hard
         | to define, and hard to evaluate. "Easy to use" or "can be used
         | within 10 minutes" or "cleans up this current order form" are
         | easy to state but hard to rate and/or hard to actionably
         | implement as metrics.
         | 
         | I've built large, deep product evaluation frameworks, and it is
         | 100% of the time a running argument with stakeholders, inside
         | and out, "well you should have measured it this way" or "I
         | think we should be targeting X not Y" or "why didn't you
         | consider Z in the metric??"
         | 
         | The Pareto Front in practice is squishy, fuzzy, and often quite
         | moist and moldy.
        
       | Whitespace wrote:
       | I have a weightlifting spreadsheet with weight on the vertical
       | axis and reps on the horizontal axis. The value of each cell is
       | the estimated 1 rep max if I accomplish that lift. In theory if
       | my e1RM is 100kg then I can lift any permutation of (weight,reps)
       | that have the same e1RM. This is akin to knowing Pareto Frontier
       | of my current strength.
       | 
       | I use conditional formatting to color cells according to the
       | probability that I can lift them--if I lifted 50kg for 10 reps
       | then I can definitely do 50kg for 9 reps, so that cell is green.
       | But if e1RM(50,10) > e1RM(40,15) then I can probably do that too
       | so it's light green. The visualization naturally becomes Pareto-
       | like.
       | 
       | If I'm feeling strong I can aim for higher weight, lower reps. Or
       | if I'm feeling weak I can close out a (weight, reps) that's below
       | my current e1RM but I haven't accomplished yet. The end result is
       | that I'm always "accomplishing" some sort of PR no matter how I
       | feel.
       | 
       | I call this e1RM Bingo.
        
         | joncrane wrote:
         | This is a cool way to gamify weightlifting. Cheers!
        
           | godwinson__4-8 wrote:
           | Indeed, GP should take a spin at turning into an app. Could
           | be worthwhile to have Claude take a first stab at a MVP.
           | 
           | If pursued, good luck!
        
             | jerkstate wrote:
             | If this is something you are interested in, I did make a
             | mobile friendly SPA similar to this: https://curvefit.app
        
               | xnx wrote:
               | Clever name
        
         | cman1444 wrote:
         | Could you please share this spreadsheet? I would really love to
         | have my own version of this.
        
           | kachnuv_ocasek wrote:
           | Just copy-paste that description to Claude and have it create
           | the spreadsheet.
        
             | Whitespace wrote:
             | The last time I tried this was back with Opus 4.6, and it
             | was ok. I tried it with Fable 5 High just now and I was
             | very impressed with the output. It took 7 minutes and one
             | turn.
             | 
             | I'm not one to believe in all the one-shot hype, but this
             | was pretty good.
        
         | wollowollo wrote:
         | Respectfully, that's a cool illustration of the idea of xRMs
         | etc but is missing the whole point of programming for higher or
         | lower reps. E.g. lower reps are more stressful / higher cost of
         | recovery but more strength-specific; high reps are better for
         | hypertrophy work. But then, any well designed program will have
         | you working across a range of rep ranges and so on.
         | 
         | Please don't make an app based on this.
        
           | jerkstate wrote:
           | > high reps are better for hypertrophy work
           | 
           | Some nuance here: the latest research shows that proximity to
           | failure is the main hypertrophy driver regardless of load and
           | rep count; high rep count makes proximity to failure harder
           | to gauge; so high load/low reps close to failure is probably
           | better for hypertrophy (there are other good reasons to do
           | higher reps/lower load work though)
        
           | bob1029 wrote:
           | The most effective (difficult) training regimens usually
           | avoid the middle of the distribution. You generally want to
           | be operating at the extremes with some rotation schedule or
           | duty cycle. High intensity interval training is an example of
           | this philosophy that occurs within a single workout session.
           | 
           | If you want the most 'optimal' form of this (aka, hell on
           | earth), you should purchase a rowing machine. Being able to
           | engage with very aggressive, full-body exercise every single
           | day without exceptions is almost like cheating biology. You
           | can maintain a 2-3x VO2 max premium over your peers with very
           | little risk of injury.
        
           | MSKJ wrote:
           | Respectfully, that's missing the point of the comment. It's a
           | fun thing to hit PRs, not everything needs a 'well actually'
        
         | jerkstate wrote:
         | I wrote this app as a SPA! It uses a curve formulation similar
         | to Brzycki, except I added a "shape" parameter (an exponent
         | gamma between 0 and 1) that slopes the 1rm downwards at the
         | right side.
         | 
         | My main finding for "pick whatever weight you want today" was
         | that picking a lot of different weights made the curve less
         | identifiable, so my latest iteration encourages you to pick a
         | ladder for a few sentinel exercises per mesocycle in order to
         | improve the statistical power. In addition, strength improves
         | more quickly at >80% of 1RM, and hypertrophy depends on
         | proximity to failure, so if you pick a lower weight, you really
         | need to go to failure, which burns you out for the rest of your
         | session, where leaving 1-2 reps in reserve is probably
         | sufficient for hypertrophy and leaves a lot more gas in the
         | tank for the rest of the session. Definitely open to
         | suggestion/discussion here.
         | 
         | https://curvefit.app (it runs on Cloudflare free tier, so I
         | won't have to start running ads or charging until I hit a
         | couple thousand users)
        
           | 747-8I wrote:
           | Great - commenting to refer to this
        
           | fudged71 wrote:
           | This is phenomenal, I'm definitely going to try this. Any
           | chance this is OSS or plans to publish in the future?
        
             | jerkstate wrote:
             | There's no particular reason it's not OSS, but my main
             | interest is collecting a lot of data on different athletes
             | and publishing original research. Most weightlifting
             | studies are small n and over a short amount of time. My
             | particular interest is how volume, load, and fatigue are
             | related to strength, endurance, and compliance over time.
             | My intention is to run it for a while, look at the data to
             | generate some hypotheses, pre-register them, then run some
             | experiments (and by that I mean just keep collecting data).
             | If someone else was particularly interested in this goal, I
             | would definitely invite them to the project. That's why it
             | was important for me to design it to be hosted for just the
             | cost of the domain name, because I don't really intend to
             | make money from it, I'm just interested in the data.
        
         | deadbabe wrote:
         | Respectfully, it's nothing new. Weightlifting industry has
         | known this concept forever, it's often just expressed as charts
         | rather than graphs, as it is easier to interpret.
         | 
         | But they go even a step further, they extend into _3
         | dimensions_ to also add body weight as a variable. So your
         | graph would really have to be a 3D volume. Because different
         | levels of body weight have different capabilities.
        
           | rafabulsing wrote:
           | Respectfully, his graph does not need 3 dimensions because
           | it's a personal spreadsheet he uses just for his own
           | training, so he can just display the data for his exact body
           | weight.
        
       | voidhorse wrote:
       | One nuance that people sometimes miss is that pareto optimality
       | in the continuous case and discrete case are distinct. Using
       | continuous case algorithms on discrete feasible set optimization
       | problems will make you miss the interior optimal points--only
       | extremal/supported points on the positive orthant hull are
       | identified by the continuous algos.
       | 
       | Matthias Ehrgott's books on multicriteria optimization explain
       | Pareto efficiency very well without sacrificing rigor. I think
       | they do a better job than this article.
        
       | stevefan1999 wrote:
       | I wonder why LLM love this word so much. Same as mint, seam,
       | tier.
        
         | amingilani wrote:
         | _A seam is a place where you can alter behavior in your program
         | without editing in that place_
         | 
         | "Chapter 4: The Seam Model", Michael C. Feathers, Working
         | Effectively with Legacy Code
        
       | joncrane wrote:
       | Question: in auto racing, could one have a Pareto Front balancing
       | single lap pace (qualifying optimization) and race pace (pace
       | over an entire stint of e.g. 20+ laps)?
        
         | transitorykris wrote:
         | You'd be looking at fuel level affecting choices of ride
         | height, brake bias, etc. Possibly changes in line and distance
         | travelled too. But, I'm curious how psychology can fit in here
         | (or not. How do you measure it?). Driver concentration and
         | confidence are important when trimming out aero or other
         | adjustments for single lap flyers.
        
       | hnnbxu2nwi wrote:
       | The lesson landed
        
       | cpa wrote:
       | At $JOB, I use the Pareto frontier all the time.
       | 
       | If one option is at least as good on every relevant dimension and
       | better on one, just pick it. That's not really a trade-off, and
       | it shouldn't need escalation. Eg, if two SaaS tools cost the same
       | and have similar support, but one fits your use case better, you
       | choose that one. Otherwise, you just suck at your job!
       | 
       | The interesting decisions only start once you're already on the
       | frontier, where getting more of one thing means giving up
       | something else. If the better tool costs 50% more, now you're
       | trading capability against cost, and that may need sign-off.
       | 
       | Basically, everyone should be able to get to the frontier on
       | their own. Coordination and arbitration at higher levels of the
       | org / between different departments should happen on the
       | frontier, where the trade-offs involve several people or teams.
        
       | shermantanktop wrote:
       | I'm sadly twitchy when I hear "Pareto" - having endured numerous
       | middle managers suggesting they can deliver 80% of the scope in
       | 20% of the time (unrelated to the frontier topic here). Do that
       | at each level of an org and the nonsense multiples rapidly.
       | 
       | The 80/20 "rule," as far as I know, is meant to be descriptive
       | after the fact. It can't be used as a planning assumption. To be
       | fair to those managers, they don't really mean to be rigorous.
       | They are just trying to justify cutting scope.
        
         | MarkusQ wrote:
         | Managers trying to justify _cutting_ scope...
         | 
         | Is your planet accepting immigrants? I think I'd like it there
        
         | nonameiguess wrote:
         | That's the "Pareto Principle" whereas the frontier is talking
         | about Pareto efficiency. They have the same name because both
         | were first developed by the economist Vilfredo Pareto, but
         | they're not actually otherwise related.
        
         | bellowsgulch wrote:
         | I don't think power law distributions are the same thing.
         | However, actually, in different fields, power law distributions
         | are descriptive enough you can use them as targets for abstract
         | criteria.
        
         | CGMthrowaway wrote:
         | Using the 80/20 rule to plan, is like that other old saw "Half
         | the money I spend on advertising is wasted. The trouble is, I
         | don't know which half"
        
       | chermi wrote:
       | We used to just call that efficiency. Overusage of "pareto
       | frontier" annoys me almost as much people talking about
       | "electrons" instead of just saying electricity or power.
        
       | solomonb wrote:
       | Now I want a hat with the Agnostic Front logo but that says
       | Pareto Front.
        
       | hnfwd5lqmp wrote:
       | Simple idea, big payoff
        
       | pmarreck wrote:
       | A very useful concept to know!
        
       | myroon5 wrote:
       | (A few years outdated) AWS EC2 instance type pareto frontier:
       | 
       | https://github.com/PatMyron/cloud#compute--memory-unit-price...
        
       | dancemethis wrote:
       | The real Pareto is the lawyer who was the victim of the Telerj
       | prank call in the 80s. Don't be fooled!
        
       | kazinator wrote:
       | > _and every solution not in the set is outperformed by at least
       | one solution in the Pareto front in every objective_
       | 
       | Is that trying to say:
       | 
       | "for every solution not in the set, there exists at least one
       | objective such that at least one solution in the Pareto set beats
       | that solution in that objective" i.e. every non-Pareto-front
       | solution is beaten in some objective(s) by a Pareto-front
       | solution, however it may be unbeaten in other objectives.
       | 
       | Or is it:
       | 
       | "for every objective in the system, every solution that is not in
       | the set is beaten in that objective by one or more Pareto-set
       | solutions."
       | 
       | Or is it:
       | 
       | "For every solution not in the set, there exists at least one
       | Pareto solution which beats it in every objective."
        
         | speedstyle wrote:
         | The latter. Every solution not in the set is 'dominated'
         | (outperformed in _every_ objective) by some specific point in
         | the set.
        
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